22 g of CO₂ at 27⁰ C is mixed with 16 g of O₂ at 37⁰C. If both gases are considered as ideal, then temperature of mixture is

• 30.5⁰C

• 37⁰C

• 27⁰C

• 29.3⁰C

At a given temperature the pressure of an ideal of density p is proportional to

• ${\rho }^2$

• $\rho$

• $\frac{1}{{\mathrm{\rho }}^2}$

• $\frac{1}{\rho }$

A cylinder contains 10kg of gas at pressure of 10⁷ N/m². The quantity of gas taken out of the cylinder, if final pressure is 2.5×10⁶ N/m² will be( temperature of gas is constant)

• 15.2 kg

• 3.7 kg

• zero

• 7.5 kg

The kinetic energy of one molecule of a gas at normal temperature and pressure will be (k = 8.31 J/mole K)

• 1.7×10³ J

• 10.2×10³ J

• 3.4×10³ J

• 6.8×10³ J

A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity u = 0.5 mls. The kinetic energy of the sphere is

• 0.1 J

• 0.3 J

• 0.5 J

• 0.42 J

Pressure of an ideal gas is increased by keeping temperature constant. What is the effect on kinetic energy of molecules?

• increase

• Decrease

• No change

• Can't be determined

Pressure of an ideal gas is increased by keeping temperature constant. What is effect on kinetic energy of molecules?

• Increase

• Decrease

• No change

• Cannot be determined

For a gas $\frac{\mathrm{R}}{{\mathrm{C}}_{\mathrm{v}}}$= 0.67. This gas is made up of molecules which are

• monoatomic

• polyatomic

• mixture of diatomic and polyatomic molecules

• diatomic

59.

A horizontal tube of length l closed at both ends, contains an ideal gas of molecular weight M. The tube is rotated at a constant angular velocity ω about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If p₁ and p₂ denote the pressure at free and the fixed end respectively, then choose the correct relation

• $\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\mathrm{e}}^{\frac{{\mathrm{M\omega }}^2 {\mathrm{l}}^2}{2^{\mathrm{RT}}}}$

• $\frac{{\mathrm{p}}_1}{{\mathrm{p}}_2} = {\mathrm{e}}^{\frac{\mathrm{M} {\mathrm{\omega l}}^2}{\mathrm{RT}}}$

• $\frac{{\mathrm{p}}_1}{{\mathrm{p}}_2} = {\mathrm{e}}^{\frac{\mathrm{\omega } \mathrm{l} \mathrm{M}}{3\mathrm{RT}}}$

• $\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\mathrm{e}}^{\frac{{\mathrm{M}}^{2 }{\mathrm{\omega }}^{2 }{\mathrm{l}}^2}{3\mathrm{RT}}}$

Two rigid boxes containing different ideal gases are placed on table. Box A contains one mole of nitrogen at temperature T₀ , while box B contains 1 mole of helium at temperature 7/3 T₀. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes) then the final temperature of gases, T_f in terms of T₀ is

• $\frac{2\hspace{0.17em}{\mathrm{T}}_0}{5}$

• $\frac{3 {\mathrm{T}}_0}{5}$

• $\frac{5 {\mathrm{T}}_0}{3}$

• $\frac{9 {\mathrm{T}}_0}{7}$