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In an ideal gas at temperature $T,$ the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$ . A good estimate for $q$ is
One mole of a monoatomic ideal gas is expanded by a process described by $p V^3=C$, where $C$ is a constant. The heat capacity of the gas during the process is given by ( $R$ is the gas constant)
A gas mixture consists of $2$ moles of oxygen and 4 moles of neon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system will be $...........\,RT$
The value of $\gamma\left(=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right),$ for hydrogen, hellium and another ideal diatomic gas $X$(whose molecules are not rigid but have an additional vibrational mode), are respectively equal to
The relation between root mean square speed $\left( v _{ rms }\right)$ and most probable speed $\left( v _{ p }\right)$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300\, K$ will be
Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\frac{\gamma_1}{\gamma_2}$ is