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

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. \(\dfrac{3}{4}N_Ak_BT_2\)

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 mean free path of molecules of a gas, (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\)
3. \(r\)
4. \(\sqrt{r}\)

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 

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. \(1/2\)