The ratio of the specific heats \(\frac{C_P}{C_V}=\gamma\) in terms of degrees of freedom \((n)\) is given by:
1. \(1+1/n\)
2. \(1+n/3\)
3. \(1+2/n\)
4. \(1+n/2\)

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:

1. 2/3

2. 3/4

3. 2

4. 1/2

A monoatomic gas at a pressure p, having a volume V expands isothermally to a volume 2 V and then adiabatically to a volume 16 V. The final pressure of the gas is: (take  γ=5/3)

1. 64ρ
 

2. 32ρ
 

3. ρ/64
 

4. 16ρ 

The mean free path of molecules of a gas, (radius r) is inversely proportional to :
1. r³
 

2. r²
 

3. r
 

4. √r

The molar specific heats of an ideal gas at constant pressure and volume are denoted by C_P and C_V respectively. If γ=C_P/C_V and R is the universal gas constant, then CV is equal to

1. 1+γ/1-γ
2. R/(γ-1)
3. (γ-1)/R
4. γR

The amount of heat energy required to raise the temperature of \(1~\text{g}\) of helium from \(T_1 ~\text{K}\) to\(T_2 ~\text{K}\) is:       [Assume volume is constant]
1. \(\dfrac{3}{8}N_Ak_B(T_2-T_1)\)
2. \(\dfrac{3}{2}N_Ak_B(T_2-T_1)\)
3. \(\dfrac{3}{4}N_Ak_B(T_2-T_1)\)
4. \(\dfrac{3}{4}N_Ak_BT_2\)

If ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ denote the specific heats (per unit mass) of an ideal gas of molecular weight M

1. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\frac{\mathrm{R}}{{\mathrm{M}}^2}$                             

2. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\mathrm{R}$

3. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\frac{\mathrm{R}}{\mathrm{M}}$                               

4. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\mathrm{MR}$

At ${10}^{°}C$ the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At ${110}^{°}C$ this ratio is 

1. x

2. $\frac{383}{283}x$

3. $\frac{10}{110}x$

4. $\frac{283}{383}x$

One mole of a perfect gas in a cylinder fitted with a piston has a pressure P, volume V and temperature 273 K. If the temperature is increased by 1 K keeping pressure constant, the increase in volume is

(1) $\frac{2V}{273}$

(2) $\frac{V}{91}$

(3) $\frac{V}{273}$

(4) V

If 300 ml of a gas at 27°C is cooled to 7°C at constant pressure, then its final volume will be -

(1) 540 ml

(2) 350 ml

(3) 280 ml

(4) 135 ml