The amount of heat energy required to raise the temperature of $1\, g$ of helium from $T_1\,K$ to $T_2K$ is

Two monoatomic ideal gas at temperature $T_1$ and $T_2$ are mixed. There is no loss of energy. If the masses of molecules of the two gases are $m_1$ and $m_2$ and number of their molecules are $n_1$ and $n_2$ respectively. The temperature of the mixture will be :

The root mean-square speed $(rms)$ of oxygen molecules $(O_2)$ at a certain absolute temperature is $\upsilon $ . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the $rms$ speed would be

$1\, kg$ of a diatomic gas is at a pressure of $8 \times 10^4\, N/m^2$. The density of the gas is $4\, kg/m^3$. What is the energy of the gas due to its thermal motion ?

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 …. $m$