The efficiency of a heat engine is $\eta$ and the coefficient of performance of a refrigerator is $\beta$. Then:

The specific heat at constant pressure of a real gas obeying $PV^2=RT$ equation is:

Match the following:

List-$I$	List-$II$
$i)$ Isothermal process	$a)$ $0$
$ii)$ Isobaric process	$b)$ $\frac{1}{\gamma-1}[P_2 V_2 - P_1 V_1]$
$iii)$ Isochoric process	$c)$ $\mu RT \ln(\frac{V_2}{V_1})$
$iv)$ Adiabatic process	$d)$ $P(V_2 - V_1)$

The correct answer is:

$A$ cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in the figure.
$A$ to $B$: volume constant
$B$ to $C$: adiabatic
$C$ to $D$: volume constant
$D$ to $A$: adiabatic
$V_C = V_D = 2V_A = 2V_B$
$(a)$ In which part of the cycle is heat supplied to the engine from outside?
$(b)$ In which part of the cycle is heat given to the surrounding by the engine?
$(c)$ What is the work done by the engine in one cycle? Write your answer in terms of $P_A, P_B, V_A$.
$(d)$ What is the efficiency of the engine?
$(\gamma = 5/3, C_v = 3/2 R$ for one mole of the gas$)$

Select the correct statement for work, heat, and change in internal energy.

Suppose an ideal gas ($n$ moles) undergoes an expansion process $P = f(V)$ which passes through the point $(V_0, P_0)$. If the slope of the curve $P = f(V)$ is greater than the slope of the adiabatic curve passing through $(V_0, P_0)$,show that the gas absorbs heat at $(V_0, P_0)$.