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 gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$Q_1 = 6000 \ J, Q_2 = -5500 \ J, Q_3 = -3000 \ J, Q_4 = 3500 \ J$
$W_1 = 2500 \ J, W_2 = -1000 \ J, W_3 = -1200 \ J, W_4 = x \ J$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are:

$A$ cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in the figure. Find the heat exchanged by the engine with the surroundings for each section of the cycle. Given ${C_v} = \frac{3}{2}R$.
$(a)$ $A$ to $B$: constant volume
$(b)$ $B$ to $C$: constant pressure
$(c)$ $C$ to $D$: adiabatic
$(d)$ $D$ to $A$: constant pressure

An ideal gas at initial temperature $T_0$ and initial volume $V_0$ is expanded adiabatically to a volume $2 V_0$. The gas is then expanded isothermally to a volume $5 V_0$ and thereafter compressed adiabatically so that the temperature of the gas becomes again $T_0$. If the final volume of the gas is $\alpha V_0$,then the value of constant $\alpha$ is

For the given $P-V$ diagram of a thermodynamic system,match the curves with their respective thermodynamic processes. ($P$ = Pressure and $V$ = Volume)

Curve	Process
$I$	$a)$ Adiabatic
$II$	$b)$ Isobaric
$III$	$c)$ Isochoric
$IV$	$d)$ Isothermal

An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically. If $p_1$ and $p_2$ represent the initial pressure and final pressure respectively,and $W$ represents the net work done by the gas during the entire process,then: