A sample of ideal gas $(f=5)$ is heated at constant pressure. If an amount $140 \mathrm{J}$ of heat is supplied to the gas, find

(a) the change in internal energy of the gas and

(b) the work done by the gas.

$P-V$ curve of a diatomic gas is shown in the figure. Find the total heat given to the gas in the process $A\to B\to C$.

A monatomic gas is enclosed in a nonconducting cylinder having a piston which can move freely. Suddenly gas is compressed to $1/8$ of its initial volume. Find the final pressure and temperature if initial pressure and temperature are $P_0$ and $T_0$ respectively.

A non-conducting cylinder having volume $2V_0$ is partitioned by a fixed non-conducting wall in two equal parts. Partition is attached with a valve. The right side of the partition is a vacuum and the left part is filled with a gas having pressure and temperature $P_0$ and $T_0$ respectively. If the valve is opened find the final pressure and temperature of the two parts.

A sample of an ideal gas is taken through the cyclic process $A\to B\to C\to A$ as shown in the figure. It absorbs $50 \mathrm{J}$ of heat during the part $A\to B$, no heat during $B\to C$ and rejects $70 \mathrm{J}$ of heat during $C\to A$. If $-40 \mathrm{J}$ of work is done on the gas during the part $B\to C$.

(a) Find the internal energy of the gas at $B$ and $C$ if it is $1500 \mathrm{J}$ at $A$.

(b) Calculate the work done by the gas during the part $C\to A$

In a cycle $ABCA$ consisting of isothermal expansion $AB$, isobaric compression $BC$ and adiabatic compression $CA$, find the efficiency of cycle (Given: $T_A=T_B=400 \mathrm{K}, \gamma =1.5$)

A container of volume $1{ \mathrm{m}}^3$ is divided into two equal compartment by a partition. One of these compartments contains an ideal gas at $300 \mathrm{K}$. The other compartment is vacuum. The whole system is thermally isolated from its surroundings. The partition is removed and the gas expands to occupy the whole volume of the container. Find the new temperature.

A fixed mass of a gas is taken through a process $A\to B\to C\to A$ (as shown in the figure). Here $A\to B$ is isobaric, $B\to C$ is adiabatic and $C\to A$ is isothermal. Find efficiency of the process (take $\gamma =1.5$).