The first law of thermodynamics is a special case of:

$A$ gas can be taken from $A$ to $B$ via two different processes $ACB$ and $ADB$. When path $ACB$ is used,$60 \, J$ of heat flows into the system and $30 \, J$ of work is done by the system. If path $ADB$ is used,the work done by the system is $10 \, J$. The heat flow into the system in path $ADB$ is ..... $J$.

Consider $1 \,kg$ of liquid water undergoing a change in phase to water vapour at $100^{\circ} C$. At $100^{\circ} C$,the vapour pressure is $1.01 \times 10^5 \,N m^{-2}$ and the latent heat of vaporization is $22.6 \times 10^5 \,J kg^{-1}$. The density of liquid water is $10^3 \,kg m^{-3}$ and that of vapour is $\frac{1}{1.8} \,kg m^{-3}$. The change in internal energy in this phase change is nearly ............ $J kg^{-1}$.

The $P-V$ diagram of a system undergoing a thermodynamic transformation is shown in the figure. The work done on the system in going from $A \to B \to C$ is $50 \, J$ and $20 \, cal$ of heat is given to the system. The change in internal energy between $A$ and $C$ is ...... $J$.

$1\,kg$ of water at $100^{\circ}C$ is converted into steam at $100^{\circ}C$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{-3}\,m^3$ as a liquid to $1.671\,m^3$ as steam. The change in internal energy of the system during the process will be $........kJ$ (Given latent heat of vaporisation $= 2257\,kJ/kg$. Atmospheric pressure $= 1 \times 10^5\,Pa$)

When the amount of work done is $333 \ cal$ and the change in internal energy is $167 \ cal$,then the heat supplied is ....... $cal$.