-
The triple points of neon and carbon dioxide 24.57 K and
216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit
scales.
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Two absolute scales A and 5 have triple points of water
defined to be 200 A and 350 B. What is the relation between \[{{\text{Y}}_{\text{steel}}}\text{=2
}\!\!\times\!\!\text{
1}{{\text{0}}^{\text{11}}}\text{N}{{\text{m}}^{\text{-2}}}\text{ and}\]and \[{{Y}_{alu\min
ium}}=7\cdot 0\times \text{1}{{\text{0}}^{\text{10}}}\text{
N}{{\text{m}}^{\text{-2}}}\]?
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The electrical resistance in ohms of a certain thermometer
varies with temperature according to the approximate law \[{{T}_{F}}'-{{T}_{F}}=\frac{180}{100}\times
1=\frac{9}{5}\]
The resistances is \[273\cdot 16\] at the triple-point of
water 273.16 K, and \[1\cdot 250\times {{10}^{5}}Pa\] at the normal melting
point of lead (600.5 K). What is the temperature when the resistance is \[1\cdot
797\times {{10}^{5}}Pa\] ?
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Answer the following:
(a)
The triple-point of water is a standard fixed point in modern thermometry. Why?
What is wrong in taking the melting point of ice and the boiling point of water
as standard fixed points (as was originally done in the Celsius scale)?
(b)
There were two fixed points in the origin Celsius scale as mentioned above
which were assigned; the number \[{{0}^{o}}C\] and \[{{100}^{o}}C\]
respectively. On the absolute scale, one of the fixed points is the
triple-point of water, which on the Kelvin absolute scale is assigned the
number 273.16 K. What is the other fixed point on this (Kelvin) scale?
(c)
The absolute temperature (Kelvin scale) T is related to the temperature t, on
the Celsius scale by\[=0\cdot 5\times {{10}^{-3}}{{m}^{3}}.\]
Why
do we have 273.15 in this relation, and not 273.16?
(d) What is the temperature of the triple-point of water on
an absolute scale whose unit interval size is equal to that of the Fahrenheit
scale?
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Two ideal gas thermometers A and B use oxygen and hydrogen
respectively. The following observations are made
Temperature
Pressure thermometer A
Pressure thermometer B
Triple point of water
\[\therefore \]
\[\vartriangle V=V-V'=M\left(
\frac{1}{P}-\frac{1}{P'} \right)\]
Normal melting point of sulphur
\[\therefore \]
\[\frac{\vartriangle
V}{V}=M\left( \frac{1}{P}-\frac{1}{P'} \right)\]
(a)
What is the absolute temperature of normal melting point of sulphur as read by
thermometers A and B?
(b) What do you think is the reason for the slightly
different answers from A and B? (The thermometers are not faulty). What further
procedure is needed in the experiment to reduce the discrepancy between the two
readings.
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A steel tape 1 m long is correctly calibrated for a
temperature of \[{{27.0}^{o}}C\] . The length of a steel rod measured by this
tape is found to be 63.0 cm on a hot day when the temperature is \[{{45.0}^{o}}C\].
What is the actual length of the steel rod on that day? What is the length of
the same steel rod on a day when the temperature is \[{{27.0}^{o}}C\]?
Coefficient of linear expansion of steel \[=1.20\times {{10}^{-5}}{{\,}^{o}}{{C}^{-1}}\].
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A large steel wheel is to be fitted on to a shaft of the
same material. At \[{{27}^{o}}C\], the outer diameter of the shaft is 8.70 cm
and the diameter of the central hole in the wheel is 8.69 cm. The shaft is
cooled using 'dry ice 9. At what temperature of the shaft does the wheel slip
on the shaft? Assume coefficient of linear expansion of the steel to be
constant over the required temperature range:
\[\frac{\vartriangle V}{V}\]
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A hole is drilled in a copper sheet. The diameter of the
hole is 4.24 cm at \[{{27.0}^{o}}C\]. What is the change in the diameter of the
hole when the sheet is heated to \[{{227}^{o}}C\]? Coefficient of linear
expansion of copper\[=2\cdot 2\times {{10}^{9}}N{{m}^{-2}}.\]\[V=1\]
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is cooled to a temperature of \[-{{39}^{o}}C\], what is the
tension developed in the wire, if the diameter is 2.0 mm? Coefficient of linear
expansion of brass \[=2.0\times {{10}^{-5}}\,{{C}^{-1}},\] and Young's modulus
of brass \[{{\text{l}}_{\text{1}}}\text{=l;}{{\text{A}}_{\text{1}}}\text{=m}{{\text{m}}^{\text{2}}}\text{;}\]
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A brass rod of length 50 cm and diameter 3.0 mm is joined to
a steel rod of the same length and diameter. What is the change in length of
the combined rod at \[{{250}^{o}}C\], if the original lengths are at \[{{40}^{o}}C\]?
Coefficient of linear expansion of brass and steel are \[10x=7\cdot
35-7x\]\[x=0\cdot 4324m\] and \[=43\cdot \text{2 cm}\]\[1\cdot 0\]respectively.
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The coefficient of volume expansion of glycerine is \[-2l=2l\left[
1+\frac{{{x}^{2}}}{2{{l}^{2}}} \right]-2l=\frac{{{x}^{2}}}{l}\]\[\therefore \].
What is the fractional 1 change in density for a \[{{30}^{o}}C\]rise in
temperature?
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A 10 kW drilling machine is used to drill a bore in a small
aluminium block of mass 8.0 kg. How 11 much is the rise in temperature of the
block in 2.5 minutes assuming 50% of power is used up in heating the machine
itself or lost to the surrounding. Specific heat of aluminium \[=1\cdot
074\times {{10}^{-2}}m=1\cdot \text{074 cm}\]\[6\cdot 9\times {{10}^{7}}Pa\]
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A copper block of mass 2.5 kg is heated in a furnace to a
temperature of \[{{500}^{o}}C\]and then placed on a large ice block. What is
the maximum amount of ice that can melt. Specific heat of copper is \[m=8\cdot
0kg=8\times {{10}^{3}}kg\]\[\vartriangle T=?,\]Heat of fusion of water \[\vartriangle
T=?,\]
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ln an experiment on the specific heat of a metal, a 0.20 kg
block of the metal at \[{{150}^{o}}C\] is dropped in a copper calorimeter (of
water equivalent 0.025 kg) containing \[150\,c{{m}^{3}}\] of water at \[{{27}^{o}}C\].
The final temperature is \[{{40}^{o}}C\]. Compute the specific heat of the
metal. If heat losses to the surroundings are not negligible, is your answer
greater or smaller than the actual value of specific heat of the metal?
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Given below are observations on molar specific heats at
room temperature of some common gases.
Gas
Molar specific heat
\[m'=\frac{mc\vartriangle
T}{L}=\frac{2500\times 0\cdot 39\times 500}{335}=1500g=1\cdot 5kg\]\[0\cdot
20\]
Hydrogen
\[0\cdot 025\]
Nitrogen
\[m=0\cdot
20kg=200g\]
Oxygen
\[\vartriangle
T=150-40={{110}^{o}}C\]
Nitric oxide
\[\vartriangle
Q=mc\vartriangle T=200\times c\times 110\]
Carbon monoxide
\[w=0\cdot
025kg=25g\]
Chlorine
\[\vartriangle
T'=40-27={{13}^{o}}C\]
The measured molar specific heats of these gases are
markedly different from those for monatomic gases. Typically, molar specific
heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can
you from the somewhat larger (than the rest) value for chlorine?
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Answer the following questions based on is the P-T phase
diagram of carbon dioxide [Fig. 7(NCT).13]
(a)
At what temperature and pressure can the solid, liquid and vapour phases of \[\text{
}\!\!\times\!\!\text{ 13=175 }\!\!\times\!\!\text{ 13}\] co-exist in
equilibrium?
(b) What is the effect of decrease
of pressure on the fusion and boiling point of \[\vartriangle Q=\vartriangle
Q'\]?
(c)
What are the critical temperature and pressure on the fusion and boiling point
of\[\therefore \]?
(d)
Is \[200\times c\times 110=175\times 13\]solid liquid or gas at (a) \[-{{70}^{o}}C\]
under 1 atm, (b) \[-{{60}^{o}}C\] under 10 atm, (c) \[\left( \text{cal
mo}{{\text{l}}^{\text{-1}}}\text{ }{{\text{K}}^{\text{-1}}} \right)\]under 56
atm?
-
Answer the following questions based on the P-T phase
diagram of \[=0\cdot 5\times {{10}^{-3}}\] as given in Q.16.
(a)
\[=0\cdot 5\times {{10}^{-3}}\] at 1 atm. pressure and temperature \[-\,{{60}^{o}}C\]
is compressed isothennally. Does it go through a liquid phase?
(b)
What happens when \[=5\times {{10}^{-4}}\] at 4 atm. pressure is cooled from
room temperature at constant pressure?
(c)
Describe qualitatively the changes in a given mass of solid \[F=50,000N\] at 10
atm. pressure and temperature \[{{65}^{o}}C\] as it is heated up to room
temperature at constant pressure.
(d) \[5\times {{10}^{-4}}\] is heated to a temperature \[{{70}^{o}}C\]
and compressed isothennally. What changes in its properties do you expect to
observe?
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A child running a temperature of \[{{101}^{o}}F\] is given
an antipyrin (i.e. a medicine that lowers fever) which causes an increase in
the rate of evaporation of sweat from his body. If the fever is brought to \[{{98}^{o}}F\]
in 20 min., what is the average rate of extra evaporation caused, by the drug?
Assume evaporation mechanism to be the only way by which heat is lost. The mass
of the child is 30 kg. specific heat of human body is approximately the same as
that of water and latent heat of evaporation of water at that temperature is
about 580 cal. \[m{{m}^{2}}\]
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A cubical ice box of thermo Cole has each side = 30 cm and a
thickness of 5 cm. 4 kg of ice is put in the box. If outside temperature is \[{{45}^{o}}C\]
and coeff. of thermal conductivity \[\frac{1\cdot
05-x}{x}=\frac{{{\text{F}}_{\text{1}}}}{{{\text{F}}_{\text{2}}}}\text{=}\frac{\text{1}}{\text{2}}\]
calculate the mass of ice left after 6 hours. Take latent heat of fusion of ice
\[2\cdot 10-2x=x\]
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A brass boiler has a base area of \[m=100g=0\cdot 100kg\]
and thickness \[AD=BD={{\left( {{l}^{2}}+{{x}^{2}} \right)}^{1/2}}\] cm. It
boils water at the rate of \[\vartriangle l=\text{AD+DB-AB=2AD-AB}\]kg/min,
when placed on a gas stove. Estimate the temperature of the part of the flame
in contact with the boiler. Thermal conductivity of brass \[=2{{\left(
{{l}^{2}}+{{x}^{2}} \right)}^{1/2}}-2l=2l{{\left( 1+\frac{{{x}^{2}}}{{{l}^{2}}}
\right)}^{1/2}}\]\[-2l=2l\left[ 1+\frac{{{x}^{2}}}{2{{l}^{2}}}
\right]-2l=\frac{{{x}^{2}}}{l}\]. Heat of vaporisation of water \[\therefore \]
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Explain why:
(a)
A body with large reflectivity is a poor emitter
(b)
A brass tumbler feels much colder than a wooden tray on a chilly day.
(c)
an optical pyrometer (for measuring high temperatures) calibrated for an ideal
black body radiation gives too low a value for the temperature of a red hot
iron piece in the open, but gives a correct value for the temperature when the
same piece is in the furnace.
(d)
The earth without its atmosphere would be inhospitably cold.
(e) Heating system based on circulation of steam are more
efficient in warming a building than those on circulation of hot water.
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A body cools from \[{{80}^{o}}C\] to \[{{50}^{o}}C\] in 5
minutes. Calculate the time it takes to cool from \[{{60}^{o}}C\] to \[{{30}^{o}}C\].
The temperature of the surrounding is \[{{20}^{o}}C\].
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question_answer23)
A
bimetallic strip is made of aluminium and steel \[({{\alpha
}_{Al}}\,>\,{{a}_{steel}})\]. On heating, the strip will
(a)
remain straight
(b)
get twisted
(c)
will bend with aluminimum on concave side.
(d)
will bend with steel on concave side.
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question_answer24)
A
uniform metallic rod rotates about its perpendicular bisector with constant
angular speed. If it is heated uniformly to raise its temperature slightly.
(a)
its speed of rotation increases.
(b)
its speed of rotation decreases.
(c)
its speed of rotation remains same.
(d)
its speed increases because its moment of inertia increases.
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question_answer25)
The
graph between two temperature scales A and B is shown in Fig. Between upper
fixed point and lower fixed point there are 150 equal division on scale A and
100 on scale B. The relationship for conversion between the two scales is given
by
(a) \[\frac{{{t}_{A}}-180}{100}\,=\,\frac{{{t}_{B}}}{150}\]
(b) \[\frac{{{t}_{A}}-30}{150}\,=\,\frac{{{t}_{B}}}{100}\]
(c) \[\frac{{{t}_{B}}-180}{150}\,=\,\frac{{{t}_{A}}}{100}\]
(d) \[\frac{{{t}_{B}}-40}{100}\,=\,\frac{{{t}_{A}}}{180}\]
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question_answer26)
An
aluminium sphere is dipped into water. Which of the following is true?
(a)
Buoyancy will be less in water at \[{{0}^{o}}C\] than that in water at \[{{4}^{o}}C\].
(b)
Buoyancy will be more in water at \[{{0}^{o}}C\] than that in water at \[{{4}^{o}}C\].
(c)
Buoyancy in water at \[{{0}^{o}}C\] will be same as that in water at \[{{4}^{o}}C\].
(d)
Buoyancy may be more or less in water at \[{{4}^{o}}C\] depending on die
radius of the sphere.
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question_answer27)
As
the temperature is increased, the time period of a pendulum
(a)
increases as its effective length increases even though its centre of mass
still remains at the centre of the bob.
(b)
decreases as its effective length increases even though its centre of mass
still remains at the centre of the bob.
(c)
increases as its effective length increases due to shifting of centre of mass
below the centre of the bob.
(d)
decreases as its effective length remains same but the centre of mass shifts
above the centre of the bob.
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question_answer28)
Heat
is associated with
(a)
kinetic energy of random motion of molecules.
(b)
kinetic energy of orderly motion of molecules.
(c)
total kinetic energy of random and orderly motion of molecules.
(d)
kinetic energy of random motion in some cases and kinetic energy of orderly
motion in other.
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question_answer29)
The
radius of a metal sphere at room temperature T is R, and the coefficient w
linear expansion of die metal is \[\alpha \]. The sphere is heated a little by
a temperature \[\Delta T\] so that its new temperature is \[T+\Delta T\]. The
increase in the volume of the sphere is approximately
(a)
\[2\,\pi \,R\,\alpha \,\Delta \,T\] (b) \[\pi
\,{{R}^{2}}\,\alpha \,\Delta \,T\]
(c)
\[4\pi \,{{R}^{3}}\,\alpha \,\Delta \,T/3\] (d) \[4\pi \,{{R}^{3}}\,\alpha
\,\Delta \,T\]
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question_answer30)
A
sphere, a cube and a thin circular plate all of same material and same mass arc
initially heated to same high temperature.
(a)
Plate will cool fastest and cube the slowest
(b)
Sphere will cool fastest and cube the slowest
(c)
Plate will cool fastest and sphere the slowest
(d)
Cube will cool fastest and plate the slowest.
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question_answer31)
Mark
the correct option:
(a)
A system X is in thermal equilibrium with Y but not with Z. System Y and Z may
be in thermal equilibrium with each other.
(b)
A system X is in thermal equilibrium with Y but not with Z. Systems Y and Z are
not in thermal equilibrium with each other.
(c)
A system X is neither in thermal equilibrium with Y nor with Z. The systems Y
and Z must be in thermal equilibrium with each other.
(d)
A system X is neither in thermal equilibrium with Y nor with Z. The system Y
and Z may be in thermal equilibrium with each other.
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question_answer32)
?Gulab Jamuns?
(assumed to be spherical) are to be heated in an oven. They are available in
two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be
discs) are also to be heated in oven. They are also in two sizes, one twice big
(in radius) than the other. All four are put together to be heated to oven
temperature. Choose the correct option from the following:
(a)
Both size gulab jammuns will get heated in the same time.
(b)
Smaller gulab jammuns are heated before bigger ones.
(c)
Smaller pizzas are heated before bigger ones.
(d)
Bigger pizzas are heated before smaller ones.
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question_answer33)
Refer
to the plot of temperature versus time (fig.) showing the changes in the state
of ice on heating (not to scale).
Which
of the following is correct?
(a) The region AB
represents ice and water in thermal equilibrium.
(b) At B water
starts boiling.
(c) At C all the
water gas converted into steam.
(d) C to D
represents water and steam in equilibrium at boiling point.
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question_answer34)
A
glass full of hot milk is poured on the table. It beings to cool gradually.
Which of the following is correct?
(a)
The rate of cooling is constant till milk attains the temperature of the
surrounding.
(b)
The temperature of milk falls off exponentially with time.
(c)
While cooling, there is a flow of heat from milk to the surrounding as well as
from surrounding to the milk but the net flow of heat is from milk to the
surrounding and that is why it cools.
(d)
All three phenomenon, conduction, convection and radiation are responsible for
the loss of heat from milk to the surroundings.
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question_answer35)
Is
the bulb of a thermometer made of diathermic or adiabatic wall?
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question_answer36)
A students records
the initial length \[l\], change in temperature \[\Delta T\]
and change in
length \[\Delta l\] of
a road as follows :
|
S. No.
|
\[l(m)\]
|
\[\Delta
T{{(}^{o}}C)\]
|
\[\Delta l(m)\]
|
|
1.
|
2
|
10
|
\[4\times
{{10}^{-4}}\]
|
|
2.
|
1
|
10
|
\[4\times
{{10}^{-4}}\]
|
|
3.
|
2
|
20
|
\[2\times
{{10}^{-4}}\]
|
|
4.
|
3
|
10
|
\[6\times
{{10}^{-4}}\]
|
If
the first observation if correct, what can you say about observations 2, 3 and
4.
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question_answer37)
Why does a metal
bar appear hotter than a wooden bar at the same temperature? Equivalently it
also appears cooler than wooden if they are both colder than room temperature.
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question_answer38)
Calculate
the temperature which has same numeral value on Celsius and Fahrenheit scale.
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question_answer39)
These
days people use steel utensils with, copper bottom. This is supposed to be good
for uniform heating of food. Explain this effect using the fact that copper is
the better conductor.
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question_answer40)
Find
out the increase in moment of inertia I of a uniform rod (coefficient of linear
expansion \[\alpha \]) about its perpendicular bisector when its temperature is
slightly increased by \[\Delta T\].
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question_answer41)
During
summers in India, one of the common practice to keep cool is to make ice balls
of crushed ice, dip it in flavoured sugar syrup and sip it. For this a stick is
inserted into crushed ice and is squeezed in the palm to make it into the ball.
Equivalently in winter in those areas where it snows, people make snow balls
and throw around. Explain the formation of ball out of crushed ice or snow in
the light of P-T diagram of water.
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question_answer42)
100
g of water is supercooled to \[-{{10}^{o}}C\]. At this point, due to some
disturbance mechanised or otherwise some of it sudden freezes to ice. What will
be die temperature of the resultant mixture and how much may would freeze?
\[[{{S}_{\omega
}}=\,1\,\,cal/g{{/}^{o}}C\,\,\text{and}\,\,{{L}^{w}}_{Fusion}=80\,cal/g]\]
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question_answer43)
One
day in the morning, Ramesh filled up 1/3 bucket of hot water from geyser, to
take bath. Remaining 2/3 was to be filled by cold water (at room temperature)
to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to
something which would take some time, say 5-10 minutes before he could take
bath. Now he had two options: (i) fill the remaining bucket completely by cold
water and then attend to the work, (ii) first attend to the work and fill the
remaining bucket just before taking bath. Which option do you think would have
kept water warmer? Explain.
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question_answer44)
We
would like to prepare a scale whose length does not change with temperature. It
is proposed to prepare a unit scale of this type whose length remains, say 10
10 cm. We can use a bimetallic strip made of brass and iron each of different
length whose length (both components) would change in such a way that
difference between their lengths remain constant. If \[{{\alpha
}_{iron}}=\,1.2\times \,{{10}^{-5}}/K\] and \[{{\alpha }_{brass}}=\,1.8\times
\,{{10}^{-5}}/K,\] what
should be take as length of each strip?
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question_answer45)
We
would like to make a vessel whose volume does not change with temperature (take
a hint from the problem above). We can use brass and iron \[({{\beta
}_{ubrass}}=6\times {{10}^{-5}}/K\] and \[{{\beta }_{urion}}=3.55\,\,\times
\,{{10}^{-5}}/K)\] to
create a volume of 100 cc. How do you think you can achieve this?
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question_answer46)
Calculate
the stress developed inside a tooth cavity filled with copper when hot tea at
temperature of \[{{57}^{o}}C\] is drunk. You can take body (tooth) temperature to be \[{{37}^{o}}C\]
and \[\alpha
=\,1.7\,\times \,{{10}^{-5}}{{/}^{0}}C,\,\] bulk modulus for copper \[=140\times
{{10}^{9}}\,N/{{m}^{2}}\].
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question_answer47)
A
rail track made of steel having length 10 m is clamped on a railway line at its
two ends. On a summer day due to rise in temperature by \[{{20}^{o}}C\], it is
deformed as shown in figure. Find \[x\] (displacement of the centre) if \[{{\alpha
}_{steel}}\,=1.2\,\times \,{{10}^{-5}}{{/}^{o}}C.\]
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question_answer48)
A
thin rod having length \[{{L}_{0}}\] at \[{{0}^{o}}C\]and coefficient of linear
expansion \[\alpha \] has
its two ends maintained at temperature \[{{\theta }_{1}}\] and \[{{\theta
}_{2}}\], respectively. Find its new length.
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question_answer49)
According
to Stefan?s law of radiation, a black body radiates energy \[\sigma {{T}^{4}}\]
from its unit
surface area every second where T is the surface temperature of the black body
and \[\sigma =5.67\,\times {{10}^{-8}}\,W/{{m}^{2}}{{K}^{4}}\] is known as
Stefan?s constant. A nuclear weapon may be thought of as a ball of radius 0.5
m. When detonated, it reaches temperature of \[{{10}^{6}}\,K\] and can be treated
as a black body.
(a)
Estimate the power it radiates.
(b)
If surrounding has water at \[{{30}^{o}}C\], how much water can 10% of the
energy produced evaporate in 1 s?
[\[{{S}_{\omega
}}\,=4186.0J/kg\,\,K\]and \[{{L}_{\upsilon }}\,=22.6\times \,{{10}^{5}}\,J/kg\]]
(c)
If all this energy U is in the form of radiation, corresponding momentum is p =
U/c. How much momentum per unit time does it impart on unit area at a distance
of 1 km?
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