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 ...... $J$.

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 $k$.

$A$ gas is compressed at a constant pressure of $50 \,N/m^2$ from a volume of $10 \,m^3$ to a volume of $4 \,m^3$. Energy of $100 \,J$ is then added to the gas by heating. Its internal energy is

$1 \ cc$ of water at its boiling point $(100^{\circ} \ C)$ is converted into steam by supplying $540 \ \text{calories}$ of heat. The volume of steam is $1671 \ cc$. If atmospheric pressure is $1.013 \times 10^5 \ \text{Nm}^{-2}$ and $J = 4.18 \ \text{joule/cal}$, the approximate value of heat required to overcome the molecular attraction is ........ $\text{cal}$.

Which of the following does not follow the first law of thermodynamics? $(W = \text{work}, Q = \text{heat}, \Delta U = \text{change in internal energy})$

$A$ container contains $1 \text{ mole}$ of a gas with molar mass $M$ and adiabatic index $\gamma = C_P/C_V$. The container is moving with a velocity $v$. When it suddenly stops,the kinetic energy of the container is converted into the internal energy of the gas. The rise in the temperature of the gas is: