The $p-V$ diagram of a system undergoing thermodynamic changes is as shown in the figure. The work done by the system in going from $A \rightarrow B \rightarrow C$ is $30 \,J$. If $68 \,J$ of heat is given to the system,then the change in the internal energy of the system between $A$ and $C$ is (in $\,J$)

The $P-V$ diagram of a system undergoing a thermodynamic transformation is shown in the figure. The work done by the system in going from $A \to B \to C$ is $30 \ J$ and $40 \ J$ of heat is given to the system. The change in internal energy between $A$ and $C$ is ....... $J$.

Density of water at $4 ^\circ C$ and $20 ^\circ C$ are $1000 \ kg/m^3$ and $998 \ kg/m^3$ respectively. The increase in internal energy of $4 \ kg$ water when it is heated from $4 ^\circ C$ to $20 ^\circ C$ is . . . . . . $J$. (Specific heat capacity of water $= 4.2 \ kJ/kg \cdot K$ and $1$ atmospheric pressure $= 10^5 \ Pa$)

If $\Delta Q$ and $\Delta W$ represent the heat supplied to the system and the work done on the system respectively,then the first law of thermodynamics can be written as,where $\Delta U$ is the change in internal energy.

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $30 \,J$ of heat and $10 \,J$ of work is done on the gas. If the initial internal energy of the gas was $10 \,J$,then the final internal energy will be: (in $\,J$)

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