
Inside a cylinder closed at both ends is a movable piston. On one side of the piston is a mass m of a gas, and on the other side a mass 2m of the same gas. What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? The temperature is the same throughout.
A)
1/4 done
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B)
1/2 done
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C)
2/3 done
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D)
1/3 done
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Two thermally insulated vessels 1 and 2 are filled with air at temperature \[{{T}_{1}},\,{{T}_{2}};\] volumes \[{{V}_{1}},\,{{V}_{2}}\] and pressures \[{{P}_{1}},\,{{P}_{2}},\] respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
A)
\[{{T}_{1}}={{T}_{2}}\] done
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B)
\[({{T}_{1}}+{{T}_{2}})/2\] done
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C)
\[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\] done
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D)
\[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\] done
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A mixture of two gases X and Y is enclosed, at constant temperature. The relative molecular mass of X, which is diatomic, is 8 times that of Y which is monoatomic. What is the ratio of the r.m.s speed of molecules of Y to that of molecules of X?
A)
2 done
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B)
\[2\sqrt{2}\] done
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C)
4 done
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D)
8 done
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Which of the following parameters does not characterize the thermodynamic state of matter?
A)
Temperature done
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B)
Pressure done
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C)
Work done
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D)
Volume done
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1 mole of a gas with \[\gamma =\text{7/5}\] is mixed with 1 mole of a gas with \[\gamma =5\text{/3,}\] then the value of \[\gamma \] for the resulting mixture is
A)
7/5 done
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B)
2/5 done
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C)
3/2 done
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D)
12/7 done
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In a closed vessel, pressure increases by 0.4% when temperature increases by
. What is the initial temperature?
A)
250 K done
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B)
\[250{}^\circ C\] done
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C)
25 K done
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D)
\[25{}^\circ C\] done
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Three perfect gases at absolute temperatures \[{{T}_{1}},\,{{T}_{2}}\] and \[{{T}_{3}}\] are mixed. The masses of molecules are \[{{m}_{1}},\,{{m}_{2}}\] and \[{{m}_{3}}\] and the number of molecules are \[{{n}_{1}},\,{{n}_{2}}\] and \[{{n}_{3}},\] respectively. Assuming no loss of energy, the final temperature of the mixture is
A)
\[\frac{({{T}_{1}}+{{T}_{2}}+{{T}_{3}})}{3}\] done
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B)
\[\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}\] done
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C)
\[\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}T_{2}^{2}+{{n}_{3}}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\] done
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D)
\[\frac{n_{1}^{2}T_{1}^{2}+n_{3}^{2}T_{2}^{2}+n_{3}^{2}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\] done
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The pressure P, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2P, volume \[\frac{V}{4}\] and temperature 2T, then the ratio of, the number of molecules in the jar A and B will be
A)
1 : 1 done
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B)
1 : 2 done
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C)
2 : 1 done
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D)
4 : 1 done
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Let \[\overline{v},\,{{v}_{rms}}\] and \[{{v}_{p}}\] respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T, the mass of a molecule is m. Then
A)
\[{{v}_{p}}<\overline{v}<{{v}_{rms}}\] done
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B)
The average kinetic energy of a molecule is \[\frac{3}{4}mv_{p}^{2}\] done
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C)
No molecule can have speed greater than \[\sqrt{2}{{v}_{rms}}\] done
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D)
No molecule can have speed less than \[{{v}_{p}}/\sqrt{2}\] done
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Two spherical vessels of equal volume are connected by a narrow tube. The apparatus contains an ideal gas at 1 atm and 300 K. Now, if one vessel is immersed in a bath of constant temperature 600K and other in a bath of constant temperature 300K, then common pressure will be
A)
1 atm done
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B)
4/5 atm done
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C)
4/3 atm done
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D)
3/2 atm done
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An adiabatic vessel contains \[{{n}_{1}}=3\] moles of a diatomic gas. The moment of inertia of each molecule is \[I=2.56\times {{10}^{46}}\,kg\,\,{{m}^{2}}\] and root mean angular velocity is\[{{\omega }_{0}}=5\times {{10}^{12}}\,rad/s\]. The temperature of the gas in the vessel is
A)
250 K done
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B)
500 K done
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C)
1000 K done
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D)
1500 K done
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A vessel containing 1 mol of \[{{O}_{2}}\] gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing 1 mol of \[He\] gas (molar mass 4) at temperature 2T has a pressure of
A)
P/8 done
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B)
2P done
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C)
3P done
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D)
8P done
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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 \[{{O}_{2}}\] molecule to that per \[{{N}_{2}}\] molecule is
A)
1 : 1 done
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B)
1 : 2 done
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C)
2 : 1 done
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D)
Depends on the moments of inertia of the two molecules done
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DIRECTION: Read the passage given below and answer the questions that follows: 
A diathermic piston divides adiabatic cylinder volume \[{{V}_{0}}\] into two equal parts as shown in the figure. Both parts contains ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are \[{{P}_{0}}\] and v while that in right compartment are \[2{{P}_{0}}\] and \[2{{T}_{0}}\]. Initially the piston is kept fixed and the system is allowed acquire a state of thermal equilibrium. 


The pressure in left compartment after thermal equilibrium is achieved is 
A)
\[{{P}_{0}}\] done
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B)
\[\frac{3}{2}{{P}_{0}}\] done
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C)
\[\frac{4}{3}{{P}_{0}}\] done
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D)
None of these done
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DIRECTION: Read the passage given below and answer the questions that follows: 
A diathermic piston divides adiabatic cylinder volume \[{{V}_{0}}\] into two equal parts as shown in the figure. Both parts contains ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are \[{{P}_{0}}\] and v while that in right compartment are \[2{{P}_{0}}\] and \[2{{T}_{0}}\]. Initially the piston is kept fixed and the system is allowed acquire a state of thermal equilibrium. 


The heat that flown from right compartment to left compartment before thermal equilibrium is achieved is 
A)
\[{{P}_{0}}{{V}_{0}}\] done
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B)
\[\frac{3}{4}{{P}_{0}}{{V}_{0}}\] done
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C)
\[\frac{3}{8}{{P}_{0}}{{V}_{0}}\] done
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D)
\[\frac{2}{3}{{P}_{0}}{{V}_{0}}\] done
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DIRECTION: Read the passage given below and answer the questions that follows: 
A diathermic piston divides adiabatic cylinder volume \[{{V}_{0}}\] into two equal parts as shown in the figure. Both parts contains ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are \[{{P}_{0}}\] and v while that in right compartment are \[2{{P}_{0}}\] and \[2{{T}_{0}}\]. Initially the piston is kept fixed and the system is allowed acquire a state of thermal equilibrium. 


If the pin which was keeping the piston fixed is removed and the piston is allowed to slide slowly such that a state of mechanical equilibrium is achieved. The volume of left compartment when piston is in equilibrium is 
A)
\[\frac{3}{4}{{V}_{0}}\] done
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B)
\[\frac{{{V}_{0}}}{4}\] done
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C)
\[\frac{{{V}_{0}}}{2}\] done
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D)
\[\frac{2}{3}{{V}_{0}}\] done
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A flask is filled with 13 gm of an ideal gas at \[27{}^\circ C\] and its temperature is raised to \[52{}^\circ C\]. The mass of the gas that has to be released to maintain the temperature of the gas in the flask at \[52{}^\circ C\] and the pressure remaining the same is
A)
2.5 g done
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B)
2.0 g done
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C)
1.5 g done
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D)
1.0 g done
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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 contains only \[{{O}_{2}},B\] only\[{{N}_{2}},\] and \[{{O}_{2}}\] mixture of equal quantities of \[{{O}_{2}}\] and \[{{N}_{2}}\]. If the average speed of the \[{{O}_{2}}\]molecules in vessel A is \[{{V}_{1}}\] that of the \[{{N}_{2}}\] molecules in vessel B is \[{{V}_{2}}\] then the average speed of the \[{{O}_{2}}\] molecules in vessel C is (where M is the mass of an oxygen molecule)
A)
\[({{V}_{1}}+{{V}_{2}})/2\] done
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B)
\[{{V}_{1}}\] done
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C)
\[{{({{V}_{1}}{{V}_{2}})}^{1/2}}\] done
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D)
\[\sqrt{3kT/M}\] done
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The graph which represents the variation of mean kinetic energy of molecules with temperature \[{{t}^{o}}C\] is
A)
B)
C)
D)
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40 calories of heat is needed to raise the temperature of 1 mol of an ideal monoatomic gas from \[20{}^\circ C\] to \[30{}^\circ C\] at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R = 2 cal/mol/K) is
A)
20 cal done
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B)
40 cal done
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C)
60 cal done
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D)
80 cal done
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From the following statements, concerning ideal gas at any given temperature T, select the correct one(s)
A)
The coefficient of volume expansion at constant pressure is same for all ideal gases done
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B)
In a gaseous mixture, the average translational kinetic energy of the molecules of each component is same done
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C)
The mean free path of molecules increases with the decrease in pressure done
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D)
The average translational kinetic energy per molecule of oxygen gas is 3KT (K being Boltzmann constant) done
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Certain perfect gas is found to obey \[P{{V}^{3/2}}=\] constant during adiabatic process. If such a gas at initial temperature T is adiabatically compressed to half the initial volume, its final temperature will be
A)
\[\sqrt{2}\,\cdot T\] done
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B)
2T done
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C)
\[2\sqrt{2}\,\cdot T\] done
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D)
4T done
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The molecules of a given mass of gas have a \[rms\] velocity of 200 m/s at \[{{27}^{o}}C\] and \[1.0\times {{10}^{5}}\,N/{{m}^{2}}\] pressure. When the temperature is \[127{}^\circ C\] and pressure is \[0.5\times {{10}^{5}}\,N/{{m}^{2}},\] the \[rms\] velocity in m/s will be
A)
\[\frac{100\sqrt{2}}{3}\] done
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B)
\[100\sqrt{2}\] done
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C)
\[\frac{400}{\sqrt{3}}\] done
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D)
None of these done
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The quantity \[\frac{PV}{KT}\] for an ideal gas represent (k = Boltzmann's constant)
A)
number of moles of the gas done
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B)
total mass of the gas done
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C)
number of molecules in the gas done
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D)
density of the gas done
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The value of \[{{C}_{p}}{{C}_{v}}=1.00R\] for a gas in state A and \[{{C}_{p}}{{C}_{v}}=1.06R\] in another state. If \[{{P}_{A}}\] and \[{{P}_{B}}\] denote the pressure and \[{{T}_{A}}\] and \[{{T}_{B}}\] denote the temperatures in the two states, respectively, then
A)
\[{{P}_{A}}={{P}_{B}},\,{{T}_{A}}>{{T}_{B}}\] done
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B)
\[{{P}_{A}}>{{P}_{B}},\,{{P}_{A}}={{T}_{B}}\] done
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C)
\[{{P}_{A}}<{{P}_{B}},\,{{P}_{A}}>{{P}_{B}}\] done
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D)
\[{{P}_{A}}>{{P}_{B}},\,{{T}_{A}}<{{T}_{B}}\] done
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\[22\,g\] of \[C{{O}_{2}}\] at \[{{27}^{o}}C\] is mixed with \[16\,g\] of \[{{O}_{2}}\] at \[37{}^\circ C\]. The temperature of the mixture is
A)
\[32{}^\circ C\] done
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B)
\[27{}^\circ C\] done
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C)
\[37{}^\circ C\] done
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D)
\[30.5{}^\circ C\] done
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A gas mixture consists of 2 mol of oxygen and 4 mol of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
A)
4 RT done
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B)
15 RT done
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C)
9 RT done
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D)
11 RT done
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At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at \[47{}^\circ C\]?
A)
80 K done
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B)
3 K done
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C)
 73 K done
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D)
20 K done
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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats \[\gamma \]. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
A)
\[\frac{(\gamma 1)}{2(\gamma +1)R}M{{v}^{2}}K\] done
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B)
\[\frac{(\gamma 1)}{2\gamma }M{{v}^{2}}K\] done
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C)
\[\frac{\gamma M{{v}^{2}}}{2R}K\] done
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D)
\[\frac{(\gamma 1)}{2R}M{{v}^{2}}K\] done
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A container has \[{{n}_{1}}\] moles of a monoatomic gas and \[{{n}_{2}}\] moles of a diatomic gas. The molar specific heat capacity at constant volume \[({{C}_{v}})\] of the mixture is found to be 2R. Then the ratio \[{{n}_{1}}/{{n}_{2}}\] is
A)
3/5 done
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B)
5/3 done
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C)
1 done
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D)
none of these done
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A box contains N molecules of a perfect gas at temperature \[{{T}_{1}}\] and pressure \[{{P}_{1}}\]. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is \[{{P}_{2}}\] and temperature \[{{T}_{2}},\] then
A)
\[{{P}_{2}}=P,\,\,{{T}_{2}}={{T}_{1}}\] done
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B)
\[{{P}_{2}}={{P}_{1}},\,{{T}_{2}}=\frac{{{T}_{1}}}{2}\] done
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C)
\[{{P}_{2}}=2{{P}_{1}},\,{{T}_{2}}={{T}_{1}}\] done
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D)
\[{{P}_{2}}=2{{P}_{1}},\,{{T}_{2}}=\frac{{{T}_{1}}}{2}\] done
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A partition divides a container having insulated walls into two compartments I and II. The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statement is correct, with reference to the final equilibrium position?
A)
The Pressure in the two compartments are unequal. done
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B)
Volume of compartment I is \[\frac{2V}{5}\] done
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C)
Volume of compartment II is\[\frac{12\,V}{5}\] done
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D)
Final pressure in compartment I is \[\frac{4P}{3}\] done
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During an experiment an ideal gas obeys an additional equation of state \[{{P}^{2}}V=\text{constant}\text{.}\] The initial temperature and volume of gas are T and V, respectively. When it expands to volume 2V, then its temperature will be
A)
T done
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B)
\[\sqrt{2}T\] done
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C)
2T done
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D)
\[2\sqrt{2}T\] done
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A monoatomic ideal gas is expanded adiabatically to n times of its initial volume. The ratio of final rate of collision of molecules with the unit area of container walls to the initial rate will be
A)
\[{{n}^{4/3}}\] done
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B)
\[{{n}^{4/3}}\] done
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C)
\[{{n}^{2/3}}\] done
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D)
\[{{n}^{2/3}}\] done
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A box has been placed on train moving uniformly with speed \[{{V}_{0}}.\] The box contains ideal gas. The value of root mean square speed with respect to an observer present in the trains is \[{{V}_{1}}.\] What will be the value of root mean square speed with respect to an observer standing on the platform?
A)
\[{{V}_{1}}+{{V}_{0}}\] done
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B)
\[{{V}_{1}}\] done
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C)
\[{{\{V_{1}^{2}+V_{0}^{2}\}}^{1/2}}\] done
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D)
None done
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