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question_answer1) A mixture of 2 moles of helium gas (atomic mass\[=4u\]), and 1 mole of argon gas (atomic mass\[=40u\]) is kept at 300 K in a container. The ratio of their rms speeds \[\left[ \frac{{{V}_{rms}}(helium)}{{{V}_{rms}}(argon)} \right]is\]
question_answer2) A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature\[27{}^\circ C\]. Amount of heat (in kJ) transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take\[R=8.3\text{ }J/Kmole\]]
question_answer3) Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atom from \[20{}^\circ C\] to \[90{}^\circ C\]. Work done (in joule) by gas is (Gas constantc \[R=8.31\text{ }J/mol-K\])
question_answer4) An ideal gas occupies a volume of \[2{{m}^{3}}\] at a pressure of \[3\times {{10}^{6}}Pa\]. The energy (in joule) of the gas is
question_answer5) An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is \[6\times {{10}^{-8}}\] s. If the pressure is doubled and temperature is increased to 500 K, the mean time (in second) between two successive collisions will be
question_answer6) If \[{{10}^{22}}\] gas molecules each of mass \[{{10}^{-26}}\] kg collide with a surface (perpendicular to it) elastically per second over an area 1 \[{{m}^{2}}\] with a speed \[{{10}^{4}}\] m/s, the pressure\[(in\text{ }N/{{m}^{2}})\]exerted by the gas molecules will be
question_answer7) The temperature (in kelvin), at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is [Boltzmann Constant \[{{k}_{B}}=1.38\times {{10}^{-23}}J/K\] Avogadro Number\[{{N}_{A}}=6.02\times {{10}^{26}}/Kg\] Radius of Earth:\[~6.4\text{ }\times \text{ }{{10}^{6}}\text{ }m\] Gravitational acceleration on\[Earth=10\text{ }m{{s}^{-2}}\]
question_answer8) For a given gas at \[1\text{ }atm\]pressure, rms speed of the molecules is 200 m/s at \[127{}^\circ C\]. At 2 atm pressure and at \[227{}^\circ C\], the rms speed (in m/s) of the molecules will be:
question_answer9) 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
question_answer10) An air bubble of volume \[1.0\text{ }c{{m}^{3}}\] rises from the bottom of a lake 40 m deep at a temperature of \[12{}^\circ C\]. To what volume (in \[{{m}^{3}}\]) does it grow, when it reaches the surface which is at a temperature of \[35{}^\circ C\]?
question_answer11) Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat (in J/mol K) of mixture at constant volume? \[\left( R=8.3J/molK \right)\]
question_answer12) A narrow uniform glass tube 80 cm long and open at both ends is half immersed in mercury. Then, the top of the tube is closed and it is taken out of mercury. A column of mercury 22 cm long then remains in the tube. What is the atmospheric pressure (in cm of mercury)?
question_answer13) A vessel of volume\[V=5.0litre\] contains 1.4 g of nitrogen at temperature,\[T=1800\text{ }K\]. Find the pressure (in N/\[{{m}^{2}}\]) of the gas if 30% of its molecules are dissociated into atoms at this temperature.
question_answer14) A gaseous mixture enclosed in a vessel consists of one gm mole of a gas A with\[(\gamma =5/3)\]and another B with\[(\gamma =7/5)\]at a temperature T. The gases A and B do not react with each other and assumed to be ideal. Find the number of gram moles of the gas if \[\gamma \] of the gaseous mixture is 19/13.
question_answer15) An oxygen cylinder of volume 30 litre has an initial gauge pressure of 15 atm and a temperature of \[27{}^\circ C\]. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drop to \[17{}^\circ C\] Estimate the mass (in kg) of oxygen taken out of the cylinder \[R=8.3Jmo{{l}^{-1}}{{K}^{-1}}\], molecule weight of oxygen \[=32.\]
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