A vertical cylinder with heat-conducting walls is closed at the bottom and is fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding’s temperature, $T_0$. The piston is moved up slowly to increase the volume of the gas to $\eta$ times. Which of the following is incorrect?

In the $P-V$ diagram shown in figure $ABC$ is a semicircle. The work done in the process $ABC$ is

Three processes form a thermodynamic cycle as shown on $P-V$ diagram for an ideal gas. Process $1 \rightarrow 2$ takes place at constant temperature $(300K$). Process $2 \rightarrow 3$ takes place at constant volume. During this process $40J$ of heat leaves the system. Process $3 \rightarrow 1$ is adiabatic and temperature $T_3$ is $275K$. Work done by the gas during the process $3 \rightarrow 1$ is ….. $J$

A gas undergoes a change of state during which $100 J$ of heat is supplied to it and it does $20 J$ of work. The system is brought back to its original state through a process during which $20 J$ of heat is released by the gas. The work done by the gas in the second process is ……. $J$

One mole of a diatomic ideal gas undergoes a cyclic process $ABC$ as shown in figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400\ K, 800\ K $ and $600\ K$ respectively. Choose the correct statement