The first law of thermodynamics is a special case of which law?

When a system is taken from thermodynamic state $i$ to $f$ along the path $iaf$ (see figure),it is found that the heat $Q$ absorbed by the system is $50 \ cal$ and the work $W$ done by the system is $20 \ cal$. Along the path $ibf$,$Q = 36 \ cal$. What is the work $W$ done along the path $ibf$ (in $cal$)?

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 ....... $J$.

When heat energy of $1500 \; J$ is supplied to a gas at a constant pressure of $2.1 \times 10^5 \; N/m^2$,its volume increases by $2.5 \times 10^{-3} \; m^3$. The increase in the internal energy of the gas in Joules is ...... $J$.

$1\,g$ of water at $100\,^{\circ}C$ and $10^5\,Pa$ pressure converts into $1841\,cm^3$ of steam at constant temperature and pressure. If the latent heat of vaporization of water is $2250\,J/g$,the change in internal energy of water in this process is ..... $J$.

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas molecules release $20 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas was $40 \ J$,then the final internal energy will be ........ $J$.