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question_answer1)
The velocity of sound in air is \[332\text{ }m\text{ }{{s}^{-1}}\] at NTP. Find the rms speed of air molecules at NTP. \[\left( \gamma =1.41 \right)\]
A)
\[484\text{ }m{{s}^{-1}}\] done
clear
B)
\[418\text{ }m{{s}^{-1}}\] done
clear
C)
\[248\text{ }m{{s}^{-1}}\] done
clear
D)
\[382\text{ }m{{s}^{-1}}\] done
clear
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question_answer2)
The density of a gas is \[6\times {{10}^{-2}}kg/{{m}^{3}}\] and the root mean square velocity of the gas molecules is 500 m/s. The pressure exerted by the gas on the walls of the vessel is
A)
\[5\times {{10}^{3}}N/{{m}^{2}}\] done
clear
B)
\[1.1\times {{10}^{-4}}N/{{m}^{2}}\] done
clear
C)
\[0.83\times {{10}^{-4}}N/{{m}^{2}}~\] done
clear
D)
\[30N/{{m}^{2}}\] done
clear
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question_answer3)
Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec. The root mean square speed of these molecules (in km/sec) is
A)
\[\sqrt{54/4}\] done
clear
B)
\[\sqrt{54/2}\] done
clear
C)
3.5 done
clear
D)
\[3\sqrt{3}\] done
clear
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question_answer4)
The absolute gas temperature at which the root mean square speed of helium molecules exceeds their most probable speed by 200 m/s is
A)
110.2 K done
clear
B)
90.2 K done
clear
C)
190.2 K done
clear
D)
100.2 K done
clear
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question_answer5)
N (< 100) molecules of a gas have velocities 1, 2, 3,........ N km/s respectively. Then ratio of rms speed and average speed is
A)
1 done
clear
B)
\[\frac{\sqrt{\left( 2N+1 \right)\left( N+1 \right)}}{6N}\] done
clear
C)
\[\frac{\sqrt{\left( 2N+1 \right)\left( N+1 \right)}}{6}\] done
clear
D)
\[2\sqrt{\frac{2N+1}{6\left( N+1 \right)}}\] done
clear
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question_answer6)
If the molecules in a tank of hydrogen have the same RMS speed as the molecules in another tank of oxygen, we may be sure that
A)
the pressures are the same done
clear
B)
the hydrogen is at the higher temperature done
clear
C)
the temperatures are the same done
clear
D)
the oxygen is at the higher temperature done
clear
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question_answer7)
\[{{H}_{2}},\,~{{O}_{2}},\text{ }{{N}_{2}}\] and \[He\] are enclosed in identical containers under the similar conditions of pressure and temperature. The gases will have
A)
same R.M.S. speed done
clear
B)
same \[\frac{K.E}{kg}\] done
clear
C)
different \[\frac{K.E.}{mole}\] done
clear
D)
same \[\frac{K.E.}{vol}\] done
clear
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question_answer8)
When do real gases approach the ideal gas behaviour?
A)
At low pressure and low temperature done
clear
B)
At low pressure and high temperature done
clear
C)
At high pressure and high temperature done
clear
D)
At high pressure and low temperature done
clear
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question_answer9)
According to the kinetic theory of gases, the pressure exerted by a gas on the wall of the container is measured as
A)
rate of change of momentum imparted to the walls per second per unit area. done
clear
B)
momentum imparted to the walls per unit area done
clear
C)
change of momentum imparted to the walls per unit volume. done
clear
D)
change in momentum per unit volume done
clear
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question_answer10)
In kinetic theory of gases, which of the following statement regarding elastic collisions of the molecules is wrong?
A)
Kinetic energy is lost in collisions done
clear
B)
Kinetic energy remains constant in collision done
clear
C)
Momentum is conserved in collision done
clear
D)
Pressure of the gas remains constant in collisions done
clear
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question_answer11)
At room temperature a diatomic gas is found to have an r. m. s. speed of \[1930\text{ }m{{s}^{-1}}\]. The gas is:
A)
\[{{H}_{2}}\] done
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B)
\[C{{l}_{2}}\] done
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C)
\[{{O}_{2}}\] done
clear
D)
\[{{F}_{2}}\] done
clear
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question_answer12)
Gases exert pressure on the walls of containing vessel because the gas molecules
A)
possess momentum done
clear
B)
collide with each other done
clear
C)
have finite volume done
clear
D)
obey gas laws done
clear
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question_answer13)
Consider a gas with density \[\rho \] and \[\overline{c}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity, then the pressure exerted by the gas is
A)
\[\frac{1}{3}\rho {{\bar{c}}^{2}}\] done
clear
B)
\[\frac{1}{3}\rho {{\left( c+\nu \right)}^{2}}\] done
clear
C)
\[\frac{1}{3}\rho {{\left( \bar{c}-\nu \right)}^{2}}\] done
clear
D)
\[\frac{1}{3}\rho {{\left( {{{\bar{c}}}^{2}}-\nu \right)}^{2}}\] done
clear
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question_answer14)
The pressure of a gas is raised from \[27{}^\circ C\]to \[927{}^\circ C.\]The root mean square speed is
A)
\[\sqrt{\left( 927/27 \right)}\] times the earlier value done
clear
B)
remain the same done
clear
C)
gets halved done
clear
D)
get doubled done
clear
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question_answer15)
Why does the pressure of an ideal gas increase when it is heated at constant volume?
A)
The gas molecules expand done
clear
B)
The molecules move at the same speed, but done
clear
C)
The molecules move faster and hit the walls more often done
clear
D)
The number of molecules of gas increases done
clear
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question_answer16)
Maxwell's velocity distribution curve is given for two different temperature. For the given curves.
A)
\[{{T}_{1}}>{{T}_{2}}\] done
clear
B)
\[{{T}_{1}}<{{T}_{2}}\] done
clear
C)
\[{{T}_{1}}\le {{T}_{2}}\] done
clear
D)
\[{{T}_{1}}={{T}_{2}}\] done
clear
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question_answer17)
Helium gas is filled in a closed vessel (having negligible thermal expansion coefficient) when it is heated from 300 K to 600 K, then average kinetic energy of helium atom will be
A)
\[\sqrt{2}\] times done
clear
B)
2 times done
clear
C)
unchanged done
clear
D)
half done
clear
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question_answer18)
The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is v, at 480 K it becomes
A)
4v done
clear
B)
2v done
clear
C)
v/2 done
clear
D)
v/4 done
clear
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question_answer19)
Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of \[{{V}_{rms}}\] of molecules and speed of sound in mixture?
A)
\[\sqrt{3/2}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[\sqrt{2/3}\] done
clear
D)
\[\sqrt{3}\] done
clear
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question_answer20)
A nitrogen molecule has some rms speed at \[0{}^\circ C\]on the surface of the earth. With this speed, it goes straight up. If there is no collisions with other molecules, the molecule will rise up to a height of
A)
82 km done
clear
B)
12.4 km done
clear
C)
10.6 km done
clear
D)
152 km done
clear
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question_answer21)
At constant volume, temperature is increased then
A)
collision on walls will be less done
clear
B)
number of collisions per unit time will increase done
clear
C)
collisions will be in straight lines done
clear
D)
collisions will not change done
clear
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question_answer22)
At what temperature is the r. m. s velocity of a hydrogen molecule equal to that of an oxygen molecule at \[47{}^\circ C\]?
A)
80 K done
clear
B)
-73 K done
clear
C)
3 K done
clear
D)
20 K done
clear
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question_answer23)
Modern vacuum pumps can evacuate a vessel down to a pressure of \[4.0\times {{10}^{-15}}\text{ }atm.\]at room temperature (300 K). Taking , \[1\text{ }atm=105\text{ }Pa\]and \[{{N}_{avogadro}}=6\times {{10}^{23}}mol{{e}^{-1}},\] the mean distance between molecules of gas in an evacuated vessel will be of the order of:
A)
0.2 urn done
clear
B)
0.2 mm done
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C)
0.2 cm done
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D)
0.2 nm done
clear
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question_answer24)
The quantity of gas in a closed vessel is halved and the velocities of its molecules are doubled. The final pressure of the gas will be
A)
P done
clear
B)
2P done
clear
C)
P/2 done
clear
D)
4P done
clear
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question_answer25)
Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative
A)
\[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}>{{V}_{3}}\] done
clear
B)
\[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}<{{V}_{3}}\] done
clear
C)
\[{{V}_{1}}={{V}_{2}}={{V}_{3}}={{V}_{4}}\] done
clear
D)
\[{{V}_{4}}>{{V}_{3}}>{{V}_{2}}>{{V}_{1}}\] done
clear
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question_answer26)
Consider a collection of a large number of dust particles each with speed v. The direction of velocity is randomly distributed in the collection. What is the magnitude of the relative velocity between a pairs in the collection?
A)
\[\frac{3v}{\pi }\] done
clear
B)
\[\frac{4v}{\pi }\] done
clear
C)
\[\frac{2v}{\pi }\] done
clear
D)
\[\frac{v}{\pi }\] done
clear
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question_answer27)
Relation between pressure (P) and energy (E) of gas is
A)
\[P=\frac{2}{3}E\] done
clear
B)
\[P=\frac{1}{3}E\] done
clear
C)
\[P=\frac{1}{2}E\] done
clear
D)
\[P=3E\] done
clear
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question_answer28)
Five gas molecules chosen at random are found to have speeds of 500, 600, 700, 800 and 900 m/s
A)
the root mean square speed and the average done
clear
B)
the root mean square speed is 14 m/s higher than the average speed. done
clear
C)
the root mean square speed is 14 m/s lower than the average speed. done
clear
D)
the root mean square speed is \[\sqrt{14}\text{ m/s}\]higher than the average speed. done
clear
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question_answer29)
Two containers A and B are partly filled with water and closed. The volume of A is twice that of B and it contains half the amount of water in B. If both are at the same temperature, the water vapor in the containers will have pressure in the ratio of
A)
1 : 2 done
clear
B)
1 : 1 done
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C)
2 : 1 done
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D)
4 : 1 done
clear
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question_answer30)
A gas mixture consists of molecules of type 1, 2 and 3, with molar masses \[{{m}_{1}}>{{m}_{2}}>{{m}_{3}}.{{v}_{rms}}\] and \[\bar{K}\] are the r. m. s. speed and average kinetic energy of the gases. Which of the following is true?
A)
\[{{({{v}_{rms}})}_{1}}<{{({{v}_{rms}})}_{2}}<{{({{v}_{rms}})}_{3}}\] and \[{{(\bar{K})}_{1}}={{(\bar{K})}_{2}}={{(\bar{K})}_{3}}\] done
clear
B)
\[{{({{v}_{rms}})}_{1}}={{({{v}_{rms}})}_{2}}={{({{v}_{rms}})}_{3}}\]and \[{{(\bar{K})}_{1}}={{(\bar{K})}_{2}}>{{(\bar{K})}_{3}}\] done
clear
C)
\[{{({{v}_{rms}})}_{1}}>{{({{v}_{rms}})}_{2}}>{{({{v}_{rms}})}_{3}}\] and \[{{(\bar{K})}_{1}}<{{(\bar{K})}_{2}}>{{(\bar{K})}_{3}}\] done
clear
D)
\[{{({{v}_{rms}})}_{1}}>{{({{v}_{rms}})}_{2}}>{{({{v}_{rms}})}_{3}}\]and \[{{(\bar{K})}_{1}}<{{(\bar{K})}_{2}}<{{(\bar{K})}_{3}}\] done
clear
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question_answer31)
One gram mole of nitrogen at \[27{}^\circ C\]and 1 aim pressure is contained in a vessel and the molecules are moving with their rms speed. The number of collisions per second which the vessel's wall is
A)
\[2\times {{10}^{27}}\] done
clear
B)
\[~2\times {{10}^{20}}\] done
clear
C)
\[2\times {{10}^{10}}\] done
clear
D)
\[~2\times {{10}^{24}}\] done
clear
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question_answer32)
In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as\[{{\text{T}}^{\text{q}}}\]. A good estimate for q is:
A)
\[\frac{1}{2}\] done
clear
B)
2 done
clear
C)
1 done
clear
D)
\[\frac{1}{4}\] done
clear
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question_answer33)
Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contain only\[{{O}_{2}}\], B only \[{{N}_{2}}\] and C a mixture of equal quantities of \[{{O}_{2}}\] and \[{{N}_{2}}\]. If the average speed of the \[{{O}_{2}}\] molecules in vessel A is that of the \[{{N}_{2}}\] molecules in vessel B is \[{{v}_{2}},\] the average speed of the \[{{O}_{2}}\] molecules in vessel C is
A)
\[\frac{{{v}_{1}}+{{v}_{2}}}{2}\] done
clear
B)
\[{{v}_{1}}\] done
clear
C)
\[{{\left( {{v}_{1}}.{{v}_{2}} \right)}^{\frac{1}{2}}}\] done
clear
D)
\[\sqrt{\frac{3kT}{M}}\] done
clear
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question_answer34)
The molecules of a given mass of a gas have r.m.s. velocity of \[200\text{ }m{{s}^{-1}}\]at \[27{}^\circ C\] and \[1.0\times {{10}^{5}}\text{ }N{{m}^{-2}}\] pressure. When the temperature and pressure of the gas are respectively, \[127{}^\circ C\]and \[0.05\times {{10}^{5}}\text{ }N{{m}^{-2}},\]the r.m.s. velocity of its molecules
A)
\[100\sqrt{2}\] done
clear
B)
\[\frac{400}{\sqrt{3}}\] done
clear
C)
\[\frac{100\sqrt{2}}{3}\] done
clear
D)
\[\frac{100}{3}\] done
clear
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question_answer35)
N molecules each of mass m of a gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of molecules of B type is \[{{v}^{2}}\] and the mean square rectangular component of the velocity of A type is denoted by \[{{\omega }^{2}}.\] Then \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\]is
A)
2 done
clear
B)
1 done
clear
C)
1/3 done
clear
D)
2/3 done
clear
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question_answer36)
The density (p)versus pressure (P) of a given mass of an ideal gas is shown at two temperatures\[~{{T}_{1}}\] and \[~{{T}_{2}}\] Then relation between \[~{{T}_{1}}\] and \[~{{T}_{2}}\] may be
A)
\[{{T}_{1}}>{{T}_{2}}\] done
clear
B)
\[{{T}_{2}}>{{T}_{1}}\] done
clear
C)
\[{{T}_{1}}={{T}_{2}}\] done
clear
D)
All the three are possible done
clear
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question_answer37)
Boyle' law is applicable for an
A)
adiabatic process. done
clear
B)
isothermal process. done
clear
C)
isobaric process. done
clear
D)
isochoric process done
clear
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question_answer38)
What will be the ratio of number of molecules of a monoatomic and a diatomic gas in a vessel, if the ratio of their partial pressures is 5 : 3?
A)
5 : 1 done
clear
B)
3 : 1 done
clear
C)
5 : 3 done
clear
D)
3 : 5 done
clear
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question_answer39)
A balloon contains \[1500\text{ }{{m}^{3}}\] of helium at \[27{}^\circ C\]and 4 atmospheric pressure. The volume of helium at \[-3{}^\circ C\] temperature and 2 atmospheric pressure will,
A)
\[1500{{m}^{3}}~\] done
clear
B)
\[~1700{{m}^{3}}\] done
clear
C)
\[1900{{m}^{3}}\] done
clear
D)
\[~2700{{m}^{3}}\] done
clear
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question_answer40)
The figure shows graph of pressure and volume of a gas at two different temperatures \[{{T}_{1}}\]and\[{{T}_{2}}\]. Which of the following inferences is correct?
A)
\[{{T}_{1}}>{{T}_{2}}\] done
clear
B)
\[{{T}_{1}}={{T}_{2}}\] done
clear
C)
\[{{T}_{1}}<{{T}_{2}}\] done
clear
D)
None of these done
clear
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question_answer41)
The average translational kinetic energy of \[{{O}_{2}}\](relative molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of \[{{N}_{2}}\] (relative molar mass 28) molecules in eV at the same temperature is
A)
0.0015 done
clear
B)
0.003 done
clear
C)
0.048 done
clear
D)
0.768 done
clear
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question_answer42)
At \[10{}^\circ C\] the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At \[110{}^\circ C\]this ratio is:
A)
x done
clear
B)
\[\frac{383}{283}x\] done
clear
C)
\[\frac{10}{110}x\] done
clear
D)
\[\frac{283}{383}x\] done
clear
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question_answer43)
Two vessels separately contain two ideal gases A and B at the same temperature. The pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:
A)
\[\frac{3}{4}\] done
clear
B)
\[2~\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{2}{3}\] done
clear
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question_answer44)
A perfect gas at \[27{}^\circ C\] is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to
A)
(a)\[327{}^\circ C\] done
clear
B)
\[200{}^\circ C\] done
clear
C)
\[54{}^\circ C\] done
clear
D)
\[300{}^\circ C\] done
clear
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question_answer45)
The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\] and 484 m/s respectively The corresponding values at 600 K are nearly (assuming ideal gas behavior)
A)
\[12.42\times {{10}^{-21}}J,928m/s\] done
clear
B)
\[8.78\times {{10}^{-21}}J,684m/s\] done
clear
C)
\[6.21\times {{10}^{-21}}J,968m/s\] done
clear
D)
\[12.42\times {{10}^{-21}}J,684m/s\] done
clear
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question_answer46)
The temperature of an air bubble while rising from bottom to surface of a lake remains constant but its diameter is doubled if the pressure on the surface is equal to h meter of mercury column and relative density of mercury is \[\rho \] then the depth of lake in meter is
A)
\[2\rho h\] done
clear
B)
\[4\rho h\] done
clear
C)
\[8\rho h\] done
clear
D)
\[7\rho h\] done
clear
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question_answer47)
Three containers of the same volume contain three different gases. The masses of the molecules are \[{{m}_{1}},{{m}_{2}}\]and \[{{m}_{3}}\]the number of\[{{N}_{1}}\], \[{{N}_{2}}\] and \[{{N}_{3}}.\] The gas pressure in the containers \[{{P}_{1}},{{P}_{2}}\] and \[{{P}_{3}}\] respectively. All the gases are now mixed and put in one of these containers. The pressure P of the mixture will be
A)
\[P<\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\] done
clear
B)
\[P=\frac{{{P}_{1}}+{{P}_{2}}+{{P}_{3}}}{3}\] done
clear
C)
\[P={{P}_{1}}+{{P}_{2}}+{{P}_{3}}\] done
clear
D)
\[P>\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\] done
clear
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question_answer48)
Temperature of a body is only on manifestation of the mean
A)
total mechanical energy of a molecule of the body done
clear
B)
potential energy of a molecule of the body done
clear
C)
rotational kinetic energy of a molecule of the body done
clear
D)
translational kinetic energy of a molecule of the body done
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question_answer49)
The mean free path of molecules of a gas, (radius
A)
\[{{r}^{3}}\] done
clear
B)
\[{{r}^{2}}\] done
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C)
\[r\] done
clear
D)
\[\sqrt{r}\] done
clear
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question_answer50)
A closed hollow insulated cylinder is filled with gas at \[0{}^\circ C\]and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \[100{}^\circ C.\]If the piston moves 5 cm, the length of the hollow cylinder is
A)
13.65 cm done
clear
B)
27.3 cm done
clear
C)
38.6 cm done
clear
D)
64.6 cm done
clear
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question_answer51)
An air bubble of volume \[{{v}_{0}}\] is released by a fish at a depth h in a lake. The bubble rises to the standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density of water is p)
A)
\[{{v}_{0}}\] done
clear
B)
\[{{v}_{0}}\left( \rho gh/p \right)\] done
clear
C)
\[{{N}_{2}}\] done
clear
D)
\[{{v}_{0}}\left( 1+\frac{\rho gh}{p} \right)\] done
clear
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question_answer52)
One kg of a diatomic gas is at a pressure of \[8\times {{10}^{4}}N/{{m}^{2}}.\] The density of the gas is4kg/m3. What is the energy of the gas due to its thermal motion?
A)
\[5\times {{10}^{4}}J\] done
clear
B)
\[6\times {{10}^{4}}J\] done
clear
C)
\[7\times {{10}^{4}}J\] done
clear
D)
\[3\times {{10}^{4}}J\] done
clear
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question_answer53)
The maximum attainable temperature of ideal gas in the process \[P={{P}_{0}}-\alpha {{V}^{2}}\] where \[{{P}_{0}}\]and \[\alpha \] are +ve constants.
A)
\[\frac{2{{P}_{0}}}{3nR}{{\left( \frac{{{P}_{0}}}{3\alpha } \right)}^{1/2}}\] done
clear
B)
\[\frac{{{P}_{0}}}{2nR}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\] done
clear
C)
\[\frac{2nR}{{{P}_{0}}}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\] done
clear
D)
\[\frac{2{{P}_{0}}}{nR}{{\left( \frac{{{P}_{0}}}{2\alpha } \right)}^{1/2}}\] done
clear
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question_answer54)
In the given (V - T) diagram, what is the relation between pressure \[{{P}_{1}}\] and\[{{P}_{2}}\]?
A)
\[{{P}_{2}}>{{P}_{1}}\] done
clear
B)
\[{{P}_{2}}<{{P}_{1}}\] done
clear
C)
Cannot be predicted done
clear
D)
\[{{P}_{2}}={{P}_{1}}\] done
clear
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question_answer55)
One mole of an ideal gas undergoes a process\[P=\frac{{{P}_{0}}}{1+{{\left( \frac{{{V}_{0}}}{V} \right)}^{2}}}\] Here \[{{P}_{0}}\] and \[{{V}_{0}}\] are constant. Change in temperature of the gas when volume is changed from \[V={{V}_{0}}\] to \[V=2{{V}_{0}}\]
A)
\[\frac{-2{{P}_{0}}{{V}_{0}}}{5R}\] done
clear
B)
\[\frac{11{{P}_{0}}{{V}_{0}}}{10R}\] done
clear
C)
\[\frac{-5{{P}_{0}}{{V}_{0}}}{10R}\] done
clear
D)
\[{{P}_{0}}{{V}_{0}}\] done
clear
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question_answer56)
The internal energy of monatomic and diatomic gases are respectively due to
A)
linear motion and rolling motion done
clear
B)
rolling motion and linear motion done
clear
C)
linear motion and rotatory motion done
clear
D)
rotatory motion and linear motion done
clear
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question_answer57)
The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be where R is the gas constant.
A)
\[PV=(5/16)RT~~\] done
clear
B)
\[PV=(5/32)RT\] done
clear
C)
\[PV=5RT~\] done
clear
D)
\[PV=(5/2)RT\] done
clear
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question_answer58)
A gas at \[27{}^\circ C\] temperature and 30 atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes
A)
\[100{}^\circ C\] done
clear
B)
\[173{}^\circ C\] done
clear
C)
\[273{}^\circ C\] done
clear
D)
\[-173{}^\circ C\] done
clear
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question_answer59)
Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is \[22{}^\circ C.\] During the day, temperature rises to \[42{}^\circ C\] and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately
A)
212 kPa done
clear
B)
209 kPa done
clear
C)
206 kPa done
clear
D)
200 kPa done
clear
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question_answer60)
Which of the following will have maximum total kinetic energy at temperature 300K?
A)
\[1kg{{H}_{2}}\] done
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B)
\[1kgHe\] done
clear
C)
\[\frac{1}{2}1kg{{H}_{2}}+\frac{1}{2}1kgHe\] done
clear
D)
\[\frac{1}{4}1kg{{H}_{2}}+\frac{3}{4}1kgHe\] done
clear
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question_answer61)
One liter of oxygen at a pressure of 1 atm, and 2 liters of nitrogen at a pressure of 0.5 atm. Are introduced in the vessel of 1 liter capacity, without any change in temperature. The total pressure would be
A)
1.5 atm. done
clear
B)
0.5 atm. done
clear
C)
2.0 atm. done
clear
D)
1.0 atm. done
clear
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question_answer62)
The degree of freedom of a molecule of a triatomic gas is
A)
2 done
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B)
4 done
clear
C)
6 done
clear
D)
8 done
clear
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question_answer63)
A polyatomic gas with n degrees of freedom has a mean energy per molecule given by
A)
\[\frac{nkT}{N}\] done
clear
B)
\[\frac{nkT}{2N}\] done
clear
C)
\[\frac{nkT}{2}\] done
clear
D)
\[\frac{3kT}{2}\] done
clear
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question_answer64)
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per molecule to that per N, molecule is
A)
1 : 1 done
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B)
1 : 2 done
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C)
2 : 1 done
clear
D)
depends on the moments of inertia of the two molecules done
clear
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question_answer65)
Two different masses m and 3m of an ideal gas are heated separately in a vessel of constant volume, the pressure P and absolute temperature T, graphs for these two cases are shown in the figure as A and B. The ratio of slopes of curves B to A is
A)
3 : 1 done
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B)
1 : 3 done
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C)
9 : 1 done
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D)
1 : 9 done
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question_answer66)
Two gases occupy two containers A and B the gas in A, of volume \[0.10{{m}^{3}}\], exerts a pressure of 1.40 MPa and that in B of volume \[0.15{{m}^{3}}\] exerts a pressure 0.7 MPa. The two containers are united by a tube of negligible volume and the gases are allowed to intermingle. Then if the temperature remains constant, the final pressure in the container will be (in MPa)
A)
0.70 done
clear
B)
0.98 done
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C)
1.40 done
clear
D)
210 done
clear
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question_answer67)
Two thermally insulated vessels 1 and 2 are filled with air at temperatures \[\] volume \[({{V}_{1}},\text{ }{{\text{V}}_{2}})\]and pressure \[({{P}_{1}},\text{ }{{\text{P}}_{2}})\] respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
A)
\[{{T}_{1}}+{{T}_{2}}\] done
clear
B)
\[({{T}_{1}}+{{T}_{2}})/2\] done
clear
C)
\[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\] done
clear
D)
\[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\] done
clear
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question_answer68)
The equation of state of a gas is given by \[\left( P+\frac{a{{T}^{2}}}{V} \right){{V}^{c}}=\left( RT+b \right)\]where a, b, c and R are constants. The isotherms can be represented \[P=A{{V}^{m}}-B{{V}^{n}},\] where A and 5 depend only on temperature and
A)
\[m=-c\text{ and }n=-1\] done
clear
B)
\[m=c\text{ and }n=-1\] done
clear
C)
\[m=-c\text{ and }n=1\] done
clear
D)
\[m=c\text{ and }n=-1\] done
clear
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question_answer69)
An ideal gas is expanding such that \[P{{T}^{2}}=\]constant. The coefficient of volume expansion of the gas is
A)
1/T done
clear
B)
2/T done
clear
C)
3/T done
clear
D)
4/T done
clear
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question_answer70)
A non-linear triatomic gas is filled inside a vessel. If 'a' fraction of moles dissociate into individual atoms, then average degree of freedom for the mixture is: (neglect vibrational degrees of freedom)
A)
\[\frac{3\alpha +6}{\alpha +1}\] done
clear
B)
\[\frac{\alpha +6}{2\alpha +1}\] done
clear
C)
\[\frac{3\alpha +6}{\alpha +2}\] done
clear
D)
\[\frac{3\alpha +6}{2\alpha +1}\] done
clear
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question_answer71)
The amount of heat energy required to raise the temperature 1g of Helium at NTP, from T,K to
A)
\[\frac{3}{2}{{N}_{a}}{{k}_{B}}\left( {{T}_{2}}-{{T}_{1}} \right)\] done
clear
B)
\[\frac{3}{4}{{N}_{a}}{{k}_{B}}\left( {{T}_{2}}-{{T}_{1}} \right)\] done
clear
C)
\[\frac{3}{4}{{N}_{a}}{{k}_{B}}\frac{{{T}_{2}}}{{{T}_{1}}}\] done
clear
D)
\[\frac{3}{8}{{N}_{a}}{{k}_{B}}\left( {{T}_{2}}-{{T}_{1}} \right)\] done
clear
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question_answer72)
The specific heat of a gas
A)
has only two values \[{{c}_{p}}\] and \[{{c}_{v}}\] done
clear
B)
has a unique value at a given temperature done
clear
C)
can have any value between 0 and \[\infty \] done
clear
D)
depends upon the mass of the gas done
clear
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question_answer73)
The specific heats at constant pressure is greater than that of the same gas at constant volume because
A)
at constant pressure work is done in expanding the gas done
clear
B)
at constant volume work is done in expanding the gas done
clear
C)
the molecular attraction increases more at constant pressure done
clear
D)
the molecular vibration increases more at constant pressure done
clear
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question_answer74)
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio \[\frac{{{C}_{p}}}{{{C}_{v}}}=\gamma \] for the gas is
A)
2 done
clear
B)
3/2 done
clear
C)
5/3 done
clear
D)
4/3 done
clear
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question_answer75)
A mixture of \[{{n}_{1}}\] moles of monoatomic gas and \[{{n}_{2}}\] moles of diatomic gas has \[\frac{{{C}_{p}}}{{{C}_{v}}}=\gamma =1.5\]then
A)
\[{{n}_{1}}={{n}_{2}}\] done
clear
B)
\[2{{n}_{1}}={{n}_{2}}\] done
clear
C)
\[{{n}_{1}}=2{{n}_{2}}\] done
clear
D)
\[2{{n}_{1}}=3{{n}_{2}}\] done
clear
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question_answer76)
Two moles of ideal helium gas are in a rubber balloon at \[30{}^\circ C.\] The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to \[35{}^\circ C.\] The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol. K)
A)
62 J done
clear
B)
104 J done
clear
C)
124 J done
clear
D)
208 J done
clear
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question_answer77)
Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is
A)
30 K done
clear
B)
18 K done
clear
C)
50 K done
clear
D)
42 K done
clear
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question_answer78)
When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is
A)
2/5 done
clear
B)
3/5 done
clear
C)
3/7 done
clear
D)
5/7 done
clear
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question_answer79)
If one mole of a monatomic gas \[\left( \gamma =\frac{5}{3} \right)\]is mixed with one mole of a diatomic gas \[\left( \gamma =\frac{7}{5} \right)\], the value of Y for mixture is
A)
1.40 done
clear
B)
1.50 done
clear
C)
1.53 done
clear
D)
3.07 done
clear
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question_answer80)
4.0 g of a gas occupies 22.4 liters at NTP. The specific heat capacity of the gas at constant volume is \[5.0J{{K}^{-1}}.\]If the speed of sound in this gas at NTP is \[952\text{ }m{{s}^{-1}},\] then the heat capacity at constant pressure is (Take gas constant \[R=8.3\text{ }J{{K}^{-1}}mo{{l}^{-1}}\])
A)
\[7.5\text{ }J{{K}^{-1}}mo{{l}^{-1}}\] done
clear
B)
\[7.0\text{ }J{{K}^{-1}}mo{{l}^{-1}}\] done
clear
C)
\[8.5J{{K}^{-1}}mo{{l}^{-1}}\] done
clear
D)
\[8.0\text{ }J{{K}^{-1}}mo{{l}^{-1}}\] done
clear
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question_answer81)
The molar specific heats of an ideal gas at constant pressure and volume are denoted by \[{{C}_{p}}\] and\[{{C}_{v}}\], respectively. If \[\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}\] and R is the universal gas constant, then Cy is equal to
A)
\[\frac{R}{\left( \gamma -1 \right)}\] done
clear
B)
\[\frac{\left( \gamma -1 \right)}{R}\] done
clear
C)
\[\gamma R\] done
clear
D)
\[\frac{1+\gamma }{1-\gamma }\] done
clear
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question_answer82)
The specific heat of \[Ar\] at constant volume is \[0.075\text{ }k{{g}^{-1}}{{K}^{-1}}.\] Calculate the atomic weight \[~\left( R=2\text{ }cal\text{ }mo{{l}^{-1}}{{K}^{-1}} \right)\]
A)
40 done
clear
B)
40.4 done
clear
C)
40.2 done
clear
D)
40.80 done
clear
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question_answer83)
A mixture of ideal gases \[{{N}_{2}}\]and He are taken in the mass ratio of 14 : 1 respectively Molar heat capacity of the mixture at constant pressure is
A)
6R/19 done
clear
B)
13R/6 done
clear
C)
6R/13 done
clear
D)
19R/6 done
clear
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question_answer84)
The ratio \[{{C}_{p}}/{{C}_{v}}\] for a gas mixture consisting of 8g of helium and 16 g of oxygen is
A)
24.2/15 done
clear
B)
15/23 done
clear
C)
27/17 done
clear
D)
17/27 done
clear
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question_answer85)
The molar specific heat at constant pressure of an ideal gas is (7/2) R. The ratio of specific heat at constant pressure to that at constant volume is
A)
8/7 done
clear
B)
5/7 done
clear
C)
9/7 done
clear
D)
7/5 done
clear
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question_answer86)
If for a gas, the gas is made up of molecules which are
A)
diatomic done
clear
B)
mixture of diatomic and polyatomic molecules done
clear
C)
monoatomic done
clear
D)
polyatomic done
clear
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question_answer87)
At very high temperatures vibrational degrees also becomes active. At such temperatures an ideal diatomic gas has a molar specific heat at constant pressure, \[{{C}_{p}}\] is
A)
3R/2 done
clear
B)
5R/2 done
clear
C)
6R/2 done
clear
D)
9R/2 done
clear
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question_answer88)
For hydrogen gas, \[{{C}_{p}}-{{C}_{v}}=a,\] and for oxygen gas, \[{{C}_{p}}-{{C}_{v}}=b,\] so the relation between a and b is given by
A)
\[a=16b\] done
clear
B)
\[16b=a\] done
clear
C)
\[a=4b~\] done
clear
D)
a=b done
clear
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question_answer89)
The value of \[{{C}_{p}}-{{C}_{v}}\] is 1.00R for a gas sample in state A and is 1.06R in state B. Let \[{{P}_{A}},{{P}_{B}}\] denote the pressure and \[{{T}_{A}},{{T}_{B}}\] denote the temperature of the states A and B respectively. Then most likely
A)
\[{{P}_{A}}<{{P}_{B}}\text{ and }{{T}_{A}}>{{T}_{B}}\] done
clear
B)
\[{{P}_{A}}>{{P}_{B}}\text{ and }{{T}_{A}}<{{T}_{B}}\] done
clear
C)
\[{{P}_{A}}={{P}_{B}}\text{ and }{{T}_{A}}<{{T}_{B}}\] done
clear
D)
\[{{P}_{A}}>{{P}_{B}}\text{ and }{{T}_{A}}={{T}_{B}}\] done
clear
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question_answer90)
A monoatomic ideal gas is taken through a reversible process whose equation is given by: \[p=k{{V}^{-\frac{1}{2}}}\] |
Where p is the pressure and V is the volume of the gas. |
The molar heat capacity of the gas in the above process, is |
A)
\[{{C}_{p}}+lR\] done
clear
B)
\[{{C}_{v}}-lR\] done
clear
C)
\[{{C}_{v}}+lR~\] done
clear
D)
\[~{{C}_{p}}+2R\] done
clear
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question_answer91)
One mole of a gas occupies 22.4 lit at N.T.P. Calculate the difference between two molar specific heats of the gas. \[J=4200J/kcal.\]
A)
1.979kcal/k mol K done
clear
B)
2.378 kcal/k mol K done
clear
C)
4.569 kcal/k mol K done
clear
D)
3.028 kcal/k mol K done
clear
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question_answer92)
For a gas, difference between two specific heats is \[5000\text{ }J/mole{}^\circ C.\]If the ratio of specific heat is 1.6, the two specific heats are in \[T=190.2K.\]
A)
\[{{C}_{p}}=1.33\times {{10}^{4}},{{C}_{V}}=2.66\times {{10}^{4}}\] done
clear
B)
\[{{C}_{p}}=13.3\times {{10}^{4}},{{C}_{V}}=8.33\times {{10}^{4}}\] done
clear
C)
\[{{C}_{p}}=1.33\times {{10}^{4}},{{C}_{V}}=8.33\times {{10}^{3}}\] done
clear
D)
\[{{C}_{p}}=2.6\times {{10}^{4}},{{C}_{V}}=8.33\times {{10}^{4}}\] done
clear
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question_answer93)
The molar specific heat at constant pressure of an ideal gas is (9/2)R. The ratio of specific heat at constant pressure to that at constant volume is
A)
1.58 done
clear
B)
1.82 done
clear
C)
1.28 done
clear
D)
1.44 done
clear
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question_answer94)
For a certain gas the ratio of specific heats is given to be y = 1.5. For this gas
A)
\[{{C}_{V}}=3R/J~\] done
clear
B)
\[{{C}_{p}}=3R/J\] done
clear
C)
\[{{C}_{p}}=5R/J\] done
clear
D)
\[{{C}_{V}}=5R/J\] done
clear
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question_answer95)
One mole of a diatomic gas is taken through the process \[P{{V}^{n}}=k,\] where n and k are constant. If the heat capacity of gas is negative, then the value of n may be
A)
\[\frac{5}{7}\] done
clear
B)
\[-\frac{5}{7}\] done
clear
C)
\[\frac{9}{7}\] done
clear
D)
\[-\frac{9}{7}\] done
clear
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question_answer96)
The relation between internal energy U, pressure P and volume V of an ideal gas in an adiabatic process is \[U=1+3PV.\]What is the value of the ratio of the molar specific heats \[\left( \frac{{{C}_{p}}}{{{C}_{V}}} \right)\]=?
A)
2/3 done
clear
B)
4/3 done
clear
C)
3/2 done
clear
D)
1 done
clear
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question_answer97)
Find the value of \[\gamma =\frac{{{C}_{p}}}{{{C}_{V}}}\] for a mixture consisting of \[{{n}_{1}}\] moles of a monoatomic gas and \[{{n}_{2}}\] moles of a gas of diatomic molecules:
A)
\[\frac{{{n}_{1}}}{{{n}_{2}}}\] done
clear
B)
\[\frac{5{{n}_{1}}+7{{n}_{2}}}{3{{n}_{1}}+5{{n}_{2}}}\] done
clear
C)
\[\frac{3{{n}_{1}}+5{{n}_{2}}}{5{{n}_{1}}+7{{n}_{2}}}\] done
clear
D)
\[\frac{7{{n}_{1}}+3{{n}_{2}}}{5{{n}_{1}}+3{{n}_{2}}}\] done
clear
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question_answer98)
Graph of specific heat at constant volume for a monatomic gas is
A)
B)
C)
D)
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question_answer99)
The K.E. of one mole of an ideal gas is E=(3/2) RT. Then \[{{C}_{p}}\]will be
A)
0.5 R done
clear
B)
0.1 R done
clear
C)
1.5 R done
clear
D)
2.5 R done
clear
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question_answer100)
For a gas sample with Np number of molecules, function N(V) is given by: \[N\left( V \right)=\frac{dN}{dV}=\left[ \frac{3{{F}_{0}}}{V_{0}^{3}} \right]{{V}^{2}}\] for \[0\le V\le {{V}_{0}}\]and \[N\left( V \right)=0\]for \[V>{{V}_{0}}\] Where \[dN\] is number of molecules in speed range V to \[V+dV.\]The rms speed of the gas molecule is
A)
\[\sqrt{\frac{2}{5}}{{V}_{0}}\] done
clear
B)
\[\sqrt{\frac{3}{5}}{{V}_{0}}\] done
clear
C)
\[\sqrt{2}{{V}_{0}}\] done
clear
D)
\[\sqrt{3}{{V}_{0}}\] done
clear
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