$A$ 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

Assertion : Heat and work are modes of energy transfer to a system resulting in change in its internal energy.
Reason : Heat and work in thermodynamics are state variables.
The correct option among the following is

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 change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is given by (where $\gamma = C_P / C_V$):

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 ............ $J kg^{-1}$.

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