The change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is (where $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume):

An ideal gas is contained in a thermally insulated rigid container. It is heated by a filament of $100 \, \Omega$ resistance by passing a current of $1 \, A$ for $5 \, \text{min}$. The change in internal energy is .... $kJ$?

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 $k$.

The first law of thermodynamics is given by:

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 ...... $J$.

$1.00 \ kg$ of liquid water at $100^{\circ} C$ undergoes a phase change into steam at $100^{\circ} C$ at $1.0 \ atm$ (take it to be $1.00 \times 10^5 \ Pa$). The initial volume of the liquid water was $1.00 \times 10^{-3} \ m^3$ which is changed to $2.001 \ m^3$ of steam. Find the change in the internal energy of the system. [Use heat of vaporization $\simeq 2000 \ kJ \ kg^{-1}$] (in $kJ$)