$A$ thermodynamic system is taken from an initial state $i$ with internal energy $U_i = 100 \ J$ to the final state $f$ along two different paths $iaf$ and $ibf$,as schematically shown in the figure. The work done by the system along the paths $ia$,$af$,$ib$ and $bf$ are $W_{ia} = 50 \ J$,$W_{af} = 200 \ J$,$W_{ib} = 50 \ J$ and $W_{bf} = 100 \ J$ respectively. The heat supplied to the system along the paths $iaf$ and $ibf$ are $Q_{iaf}$ and $Q_{ibf}$ respectively. If the internal energy of the system in the state $b$ is $U_b = 200 \ J$ and $Q_{iaf} = 500 \ J$,the ratio $Q_{ibf} / Q_{iaf}$ is:

The ratio of the slopes of isothermal and adiabatic curves is

$A$ cyclic process on an ideal monatomic gas is shown in the figure. The correct statement is:

The internal energy of the air in a room of volume $V$ at temperature $T$, with outside pressure $P$ increasing linearly with time, varies as

Match the following lists.

List-$I$	List-$II$
$A$. Zeroth law of thermodynamics	$I$. Direction of flow of heat
$B$. First law of thermodynamics	$II$. Work done is zero
$C$. Free expansion of a gas	$III$. Thermal equilibrium
$D$. Second law of thermodynamics	$IV$. Law of conservation of energy

The correct answer is:

One mole of an ideal gas is taken through a cyclic process with alternating isothermal and adiabatic curves. In the $P-V$ diagram, $AB, CD, EF$ are isothermal curves at absolute temperatures $T_1, T_2,$ and $T_3$ respectively, and $BC, DE,$ and $FA$ are adiabatic curves. If $\frac{V_B}{V_A} = 2$ and $\frac{V_D}{V_C} = 2$, then for the cycle shown in the figure, four statements are made below. (Figure is not drawn to scale)
Statement $1$: Ratio of volumes $\frac{V_E}{V_F} = 4$
Statement $2$: Magnitude of work done in isothermal compression $EF$ is $2RT_3 \ln(2)$
Statement $3$: Ratio of heat supplied to the gas in process $AB$ to heat rejected by the gas in process $EF$ is $\frac{T_1}{T_3}$
Statement $4$: Net work done by the gas in the cycle $ABCDEFA$ is $(T_1 + T_2 - 2T_3) R \ln(2)$
Find the number of correct statements given for the cyclic process followed by the gas.