$A$ system is taken from state $A$ to state $B$ along two different paths. The heat absorbed and work done by the system along these two paths are $Q_1, Q_2$ and $W_1, W_2$ respectively,then

$A$ sample of $0.1 \, g$ of water at $100^{\circ} C$ and normal pressure $(1.013 \times 10^5 \, N m^{-2})$ requires $54 \, cal$ of heat energy to convert to steam at $100^{\circ} C$. If the volume of the steam produced is $167.1 \, cc$,the change in internal energy of the sample is ....... $J$.

In a thermodynamic process,$200 \ J$ of heat is given to a gas and $100 \ J$ of work is also done on it. The change in internal energy of the gas is ........ $J$.

The internal energy change in a system that has absorbed $2 \, kcal$ of heat and done $500 \, J$ of work is ...... $J$.

$A$ gas is supplied with $1500 \; J$ of heat energy at constant pressure. If the constant pressure of the gas is $2.1 \times 10^{5} \; N/m^{2}$ and the increase in volume is $2.5 \times 10^{-3} \; m^{3}$,then the increase in the internal energy of the gas is ...... $J$.

$1 \,g$ of water at $100^{\circ} C$ is completely converted into steam at $100^{\circ} C$. $1 \,g$ of steam occupies a volume of $1650 \,cc$. (Neglect the volume of $1 \,g$ of water at $100^{\circ} C$). At the pressure of $10^5 \,N/m^2$, the latent heat of steam is $540 \,cal/g$ $(1 \,calorie = 4.2 \,joule)$. The increase in the internal energy (in joule) is: