The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:

1.	\(l\propto \dfrac{1}{d^2}\)	2.	\(l\propto d\)
3.	\(l\propto d^2 \)	4.	\(l\propto \dfrac{1}{d}\)

If \(C_P\) and \(C_V\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_P-C_V=R\)
2. \(C_P-C_V=\frac{R}{M}\)
3. \(C_P-C_V=MR\)
4. \(C_P-C_V=\frac{R}{M^2}\)

To find out the degree of freedom, the correct expression is:
1. \(f=\frac{2}{\gamma -1}\)
2. \(f=\frac{\gamma+1}{2}\)
3. \(f=\frac{2}{\gamma +1}\)
4. \(f=\frac{1}{\gamma +1}\)

The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the gas constant)
1. PV = 5 RT
2. PV = (5/2) RT
3. PV = (5/16) RT
4. PV = (5/32) RT

Uranium has two isotopes of masses \(235 \) and \(238\) units. If both are present in Uranium hexafluoride gas, which would have the larger average speed?
1. \(^{235} \mathrm{U} \mathrm{F}_{6}\)
2. \({}^{238} \mathrm{U} \mathrm{F}_{6}\)
3. Both will have the same average speed.
4. Data insufficient

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. The equation in kinetic theory \(PV = \dfrac{2}{3}E,\)$$ \(E\) is:

\(1\) mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at \(300\) K (figure). One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time:
                               

When an ideal gas is compressed adiabatically, its temperature rises: the molecules on an average have more kinetic energy than before. The kinetic energy increases:

An increase in the temperature of a gas-filled in a container would lead to: