# Choose the correct option related to the specific heat at constant volume ${C}_{V}$ - 1. ${C}_{V}=\frac{1}{2}fR$            2. ${C}_{V}=\frac{R}{\gamma -1}$ 3. ${C}_{V}=\frac{{C}_{P}}{\gamma }$                4. All of these

Subtopic:  Specific Heat |
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The curve between absolute temperature and $$\mathrm{v}^2_{rms}$$${}^{}$ is:

 1 2 3 4
Subtopic:  Types of Velocities |
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Five molecules of a gas have speeds, 1, 2, 3, 4 and 5 km${s}^{-1}$.  The value of the root mean square speed of the gas molecules is:

1. 3 km${s}^{-1}$

2. $\sqrt{11}$ km${s}^{-1}$

3. $\frac{1}{2}\sqrt{\mathrm{\pi }}$ km${s}^{-1}$

4. 3.5 km${s}^{-1}$

Subtopic:  Types of Velocities |
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The average velocity of an ideal gas molecule is:

 1 proportional to $$\sqrt{T}$$ 2 proportional to $$T^2$$ 3 proportional to $$T^3$$ 4 zero
Subtopic:  Types of Velocities |
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For a gas, $\frac{R}{{C}_{V}}=0.67$.  This gas is made up of molecules which are:                                                                   [JIPMER 2001, 02]

1. Diatomic

2. Mixture of diatomic and polyatomic molecules

3. Monoatomic

4. Polyatomic

Subtopic:  Specific Heat |
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At constant temperature, on increasing the pressure of a gas by 5% , its volume will decrease by:

1. 5%

2. 5.26 %

3. 4.26 %

4. 4.76 %

Subtopic:  Ideal Gas Equation |
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PMT - 2006
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At what temperature is the root mean square speed of molecules of hydrogen twice as that at STP?
1. $$273$$ K
2. $$546$$ K
3. $$819$$ K
4. $$1092$$ K

Subtopic:  Types of Velocities |
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At what temperature, is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at 47$°$C:[MP PET 1997, 2000; RPET 1999; AIEEE 2002; J & K CET 2004; Kerala PET 2010]

1. 20 K

2. 80 K

3. - 73 K

4. 3 K

Subtopic:  Types of Velocities |
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The average kinetic energy of a gas molecule can be determined by knowing:                                        [RPET 2000, MP PET 2010]

1. The number of molecules in the gas

2. The pressure of the gas only

3. The temperature of the gas only

4. None  of the above is enough by itself

Subtopic:  Kinetic Energy of an Ideal Gas |
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Volume, pressure, and temperature of an ideal gas are $$V$$, $$P$$, and $$T$$ respectively. If the mass of its molecule is $$m$$, then its density is: [$$k$$=Boltzmann's constant]

 1 $$mkT$$ 2 $$P \over kT$$ 3 $$P \over kTV$$ 4 $$Pm \over kT$$
Subtopic:  Ideal Gas Equation |
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