The increase in internal energy of $2$ moles of gas when its temperature is raised from $340 \ K$ to $342 \ K$ is ........ $cal$. Given $C_v = 4.96 \ cal/mole \ K$.

Given that $1\,g$ of water in liquid phase has volume $1\,cm^3$ and in vapour phase $1671\,cm^3$ at atmospheric pressure and the latent heat of vaporization of water is $2256\,J/g$,the change in the internal energy in joules for $1\,g$ of water at $373\,K$ when it changes from liquid phase to vapour phase at the same temperature is ....... $J$.

$1.00 \ kg$ of liquid water at $100^{\circ} C$ undergoes a phase change into steam at $100^{\circ} C$ at $1.0 \ atm$ (take it to be $1.00 \times 10^5 \ Pa$). The initial volume of the liquid water was $1.00 \times 10^{-3} \ m^3$ which is changed to $2.001 \ m^3$ of steam. Find the change in the internal energy of the system. [Use heat of vaporization $\simeq 2000 \ kJ \ kg^{-1}$] (in $kJ$)

$A$ system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in the figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes $I$ and $II$ respectively, then the relation between $\Delta U_1$ and $\Delta U_2$ is

An ideal gas is contained in a thermally insulated rigid container. It is heated by a filament of $100 \, \Omega$ resistance by passing a current of $1 \, A$ for $5 \, \text{min}$. The change in internal energy is .... $kJ$?

During the process $A \rightarrow B \rightarrow C$,the work done is $50 \, J$ and the heat supplied is $20 \, cal$. Find the change in internal energy between $A$ and $C$ in $J$. (in $, J$)