The change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is given by (where $\gamma = C_P / C_V$):

When $2 \ kg$ of water is boiled at atmospheric pressure,it converts into steam. The volume increases from $2 \times 10^{-3} \ m^3$ to $3.34 \ m^3$. The work done by the system is ....... $kJ$.

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:

$A$ total of $48 \,J$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ} C$. The work done by the gas is : (Given,$R=8.3 \,J \,K^{-1} \,mol^{-1}$.) (in $\,J$)

For a thermodynamic process $\delta Q = -50 \text{ calorie}$ and $W = -20 \text{ calorie}$. If the initial internal energy is $-30 \text{ calorie}$,then the final internal energy will be ....... $\text{calorie}$.

$A$ system is provided with $200 \, cal$ of heat and the work done by the system on the surroundings is $40 \, J$. Then its internal energy