Which of the following laws of thermodynamics defines the term internal energy?

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 ....... $J$.

When a system is taken from state $i$ to state $f$ along the path $iaf$,it is found that $Q = 50 \ cal$ and $W = 20 \ cal$. Along the path $ibf$,$Q = 36 \ cal$. The work done $W$ along the path $ibf$ is ....... $cal$.

The latent heat of vaporisation of water is $2240 \, J/g$. If the work done in the process of expansion of $1 \, g$ of water is $168 \, J$,then the increase in internal energy is ....... $J$.

$A$ gas is expanded from an initial state to a final state along a path that consists of $(a)$ an isothermal expansion doing $40 \,J$ work,$(b)$ an adiabatic expansion doing $W$ work,$(c)$ an isothermal expansion doing $30 \,J$ work. If the total change in the internal energy of the gas is $-20 \,J$,the work done by the gas during the adiabatic expansion $W=$ (in $\,J$)

$A$ thermodynamic system is changed from state $(P_1, V_1)$ to $(P_2, V_2)$ by two different processes. The quantity which will remain the same is