The velocities of sound at the same temperature in two monoatomic gases of densities ρ₁ and  ρ₂ and  ν₁ and  ν₂ respectively. If  ρ₁ / ρ₂ = 4, then the value of  ν₁/ ν₂  is

• 1/4

• 2

• 1/2

• 4

The average velocity of the molecules in a gas in equilibrium is

• proportional to $\sqrt{\mathrm{T}}$

• proportional to T

• proportional to T²

• equal to zero

If at the same temperature and pressure, the densities of two diatomic gases are d1 and d, respectively, the ratio of mean kinetic energy per molecule of gases will be

• 1 : 1

• ${\mathrm{d}}_1$ : ${\mathrm{d}}_2$

• $\sqrt{{\mathrm{d}}_1} : \sqrt{{\mathrm{d}}_2}$

• $\sqrt{{\mathrm{d}}_2} : \sqrt{{\mathrm{d}}_1}$

The value of the gas constant (R) calculated from the perfect gas equation is 8.32 J/g mol-K, whereas its, value calculated from the knowledge of C_P and C_v of the gas is 1.98 cal/g mol-K. From this data value of J is

• 4.16 J/cal

• 4.18 J/cal

• 4.20 J/cal

• 4.22 J/cal

A monoatomic gas supplied the heat Q very slowly keeping the pressure constant. The work done by the gas will be:

• $\frac{2}{3}\mathrm{Q}$

• $\frac{3}{5}\mathrm{Q}$

• $\frac{2}{5}\mathrm{Q}$

• $\frac{1}{5}\mathrm{Q}$

When the temperature of an ideal gas is increased from 27°C to 227°C, its rms speed is changed from 400 metre/sec to v_s. The v_s is :

• 516 m/s

• 450 m/s

• 310 m/s

• 746 m/s

Universal gas constant is :

• $\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}$

• C_p - C_v

• C_P + C_V

• $\frac{{\mathrm{C}}_{\mathrm{V}}}{{\mathrm{C}}_{\mathrm{P}}}$

A mixture of oxygen and hydrogen are filled in a vessel at a fixed temperature. The ratio of average kinetic energies of atoms of H₂ and O₂ is

• 1 : 16

• 1 : 8

• 1 : 12

• 1 : 1

The speed of sound in a gas ($\mathrm{\gamma }$=1.5) at 300 K is 340 m/s. The rms velocity of gas molecules will be

• 340  m/s

• $\frac{340}{\sqrt{2}}$ m/s

• 340$\sqrt{2}$ m/s

• 340$\sqrt{15}$ m/s

If 2 g mole of diatomic gas and 1 g mole of monoatomic gas are mixed together, then the ratio of specific heats of mixture is

• 1 : 24

• 1 : 58

• 1 : 46

• 1 : 60