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?

The $P-V$ diagram shows seven curved paths (connected by vertical paths) that can be followed by a gas. Which two of them should be parts of a closed cycle if the net work done by the gas is to be at its maximum value

A system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in figure. If $\Delta {U_1}$ and $\Delta {U_2}$ are the changes in internal energies in the processes $I$ and $II$ respectively, then

A thermodynamic system is taken form an initial state $i$ with internal energy $U_1=100 \ J$ to the final state along two different paths iaf and ibf, as schematically shown in the fire. The work done by the system along the paths $af$, ib and bf are $W _{ af }=200 \ J , W _{ ID }=50 \ J$ and $W _{ br }=100 \ J$ respectively. The heat supplied to the system along the path iaf, ib and bf are $Q_{\mid a t l} Q_{b r}$ and $Q_{10}$ respectively. If the internal energy of the sytem in the state $b$ is $U_b=$ $200 \ J$ and $Q_{l a t}=500 \ J$, the ratio $Q_{b J} / Q_{10}$ is:

A thermodynamic system is taken through cyclic process. The total work done in the process is $………\,J$