If heat energy $\Delta Q$ is supplied to an ideal diatomic gas,the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta W$. The ratio $\Delta W: \Delta U: \Delta Q$ is

The temperature-entropy $(T-S)$ diagram of a reversible engine cycle is given in the figure. Its efficiency is

Three samples $X, Y$,and $Z$ of the same gas have equal volumes and temperatures. The volume of each sample is doubled. The process is isothermal for $X$,adiabatic for $Y$,and isobaric for $Z$. If the final pressures are equal for the three samples,find the ratio of the initial pressures. (Take adiabatic exponent $\gamma = 3/2$)

For an ideal gas,which of the following statements is correct?

An ideal gas at pressure $P_0$ undergoes an isothermal expansion until its volume is $8.0$ times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is $\gamma = 4/3$, then the ratio of the average kinetic energy per molecule in this final state to that in the initial state is

$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is $\left(\gamma = \frac{5}{3}\right)$.