The change in internal energy when $20 \,g$ of a gas is heated from $25^{\circ} C$ to $35^{\circ} C$ at constant volume is (Specific heat capacity of the gas at constant volume $C_{v} = 0.2 \,cal \,g^{-1} {}^{\circ} C^{-1}$): (in $\,J$)

When unit mass of water boils to become steam at $100\,^{\circ}C$,it absorbs $Q$ amount of heat. The densities of water and steam at $100\,^{\circ}C$ are $\rho_1$ and $\rho_2$ respectively and the atmospheric pressure is $p_0$. The increase in internal energy of the water is:

$A$ thermodynamic system absorbs $2 \, kcal$ of heat and performs $500 \, J$ of work. The change in its internal energy is ......... $J$.

$A$ monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions: $(i)$ at constant volume and $(ii)$ at constant pressure. The change in internal energy of the gas is

$A$ system is given $300$ calories of heat and it does $600$ joules of work. How much does the internal energy of the system change in this process? $(J = 4.18 \text{ Joules/cal})$ (in joule)

During a thermodynamic process,the pressure of a fixed mass of gas is changed in such a way that the gas releases $20 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas is $40 \ J$,then the final internal energy is ...... $J$.