A given sample of an ideal gas occupies a volume V at a pressure p and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?

(1) p/(kT)        (2) pm / (kT)

(3) p/ (kTV)     (4) mkT

The molecules of a given mass of gas have rms velocity of 200 ms^-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10⁵ Nm^-2, rms velocity of its molecules in ms^-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√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:

(a)2/3

(b)3/4

(c)2

(d)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

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) $\frac{283}{383}x$

The ratio of two specific heats of gas $C_p/C_v$ for argon is 1.6 and for hydrogen is 1.4. Adiabatic elasticity of argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to E at the pressure :

(1) P                                       

(2) $\frac{8}{7}P$

(3) $\frac{7}{8}P$                                   

(4) 1.4P

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