When an air bubble of radius $‘r’$ rises from the bottom to the surface of a lake, its radius becomes $5r/4$ (the pressure of the atmosphere is equal to the $10 \,m$ height of water column). If the temperature is constant and the surface tension is neglected, the depth of the lake is …. $m$

An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to $10\, m$ of water, the height of water in the reservoir is ….. $m$

One mole of ideal monoatomic gas $(\gamma \, = \,5/3)$ is mixed with one mole of diatomic gas $(\gamma \, = \,7/5)$ What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/ 2 $ is given by the straight line

A gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $A_r$ at temperature $T.$ Neglecting all vibrational modes, the total internal energy of the system is