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 ....... $J$.

Consider one mole of perfect gas in a cylinder of unit cross-section with a piston attached as shown in the figure. $A$ spring (spring constant $k$) is attached (unstretched length $L$) to the piston and to the bottom of the cylinder. Initially,the spring is unstretched and the gas is in equilibrium. $A$ certain amount of heat $Q$ is supplied to the gas,causing an increase in volume from $V_0$ to $V_1$.
$(a)$ What is the initial pressure of the system?
$(b)$ What is the final pressure of the system?
$(c)$ Using the first law of thermodynamics,write down a relation between $Q, V_0, V_1, P_a$ and $k$.

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

$110\; J$ of heat is added to a gaseous system,whose internal energy change is $40\; J$,then the amount of external work done is ........ $J$.

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 ....... $J$.