Kinetic Theory ...

An ideal gas follows a process described by $$PV^2=C$$ from $$(P_1, V_1, T_1)$$ to $$(P_2, V_2, T_2)$$ (C is a constant). Then.

At what temperature hydrogen molecules will escape from the earth's surface?
(Take mass of hydrogen molecule $$ = 0.34 \times 10^{-26} $$ kg, Boltzman constant $$ = 1.38 \times 10^{-23} $$ J/K, radius of the earth $$ = 6.4 \times 10^{6} $$ and acceleration due to gravity $$ = 9.8 m/s^2 $$

If at the same temperature and pressure, the densities of two diatomic gases are $${ d }_{ 1 }$$ and $${ d }_{ 2 }$$ respectively, the ratio of mean kinetic energy per molecule of gases will be :

$$4.48L$$ of an ideal gas at S.T.P requires $$12$$ calories to raise its temperature by $${15}^{o}C$$ at constant volume. The $${C}_{p}$$ of the gas is:

In Haber's process of ammonia manufacture:
$${ N }_{ 2 }(g)+3{ H }_{ 2 }(g)\longrightarrow 2{ NH }_{ 3 }(g)$$, $$\Delta { H }_{ { 25 }^{ o }C }^{ o }=-92.2kJ$$

Molecules	$${N}_{2}(g)$$	$${H}_{2}(g)$$	$${NH}_{3}(g)$$
$${C}_{P}J{ K }^{ -1 }{ mol }^{ -1 }$$	$$29.1$$	$$28.8$$	$$35.1$$

If $${C}_{P}$$ is independent of temperature,then reaction at $${100}^{o}C$$ compared to that of $${25}^{o}C$$ will be:

The mean energy of a molecule of an ideal gas is

Two identical containers P and Q with frictionless piston contain the same ideal gas at the same temperature and the same volume. The mass of gas in P is $$m_1$$ and that in Q is $$m_2$$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $$1.5$$V. The changes pressure in P and Q are found to be $$\Delta$$p and $$2\Delta$$p respectively then.

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $$300\ K$$. The ratio of the average rotational kinetic energy per $$O_{2}$$ molecule to per $$N_{2}$$ molecule is

Equal volumes of monoatomic and diatomic gases at the same temperature are given equal quantities of heat. Then,

The temperature at which the mean KE of the molecules of gas is one-third of the mean KE of its molecules at $$180^o C$$ is