If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$,then the ratio of the efficiency of the heat engine to the coefficient of performance of the refrigerator is:

An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

An ideal gas expands from volume $V_1$ to $V_2$. This may be achieved by either of the three processes: isobaric,isothermal,and adiabatic. Let $\Delta U$ be the change in internal energy of the gas,$Q$ be the quantity of heat added to the system,and $W$ be the work done by the system. Identify which of the following statements is false for $\Delta U$?

What are the limitations of the first law of thermodynamics?

$A$ thermodynamic cycle of an ideal gas is shown in the figure. Choose the correct option which represents the same cycle.

What is an isothermal process, adiabatic process, and isobaric process? Write the first law of thermodynamics for an ideal gas.