Two samples $A$ and $B$ of gas are initially at the same pressure and temperature. They are compressed from volume $V$ to $\frac{V}{2}$ ($A$ isothermally and $B$ adiabatically). The relation between the pressure of gas $A$ $(P_A)$ and the pressure of gas $B$ $(P_B)$ is:

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cycle given in the figure? Where, $1 \rightarrow 2$ is adiabatic.

$A$ monoatomic gas at a pressure $P$,having a volume $V$ expands isothermally to a volume $4V$ and then adiabatically to volume $16V$. The final pressure of the gas is (Take $\gamma = \frac{5}{3}$)

Match List-$I$ with List-$II$.

$A$. Isobaric	$I$. $\Delta Q = \Delta W$
$B$. Isochoric	$II$. $\Delta Q = \Delta U$
$C$. Adiabatic	$III$. $\Delta Q = 0$
$D$. Isothermal	$IV$. $\Delta Q = \Delta U + P \Delta V$

$\Delta Q = \text{Heat supplied}$,$\Delta W = \text{Work done by the system}$,$\Delta U = \text{Change in internal energy}$,$P = \text{Pressure of the system}$,$\Delta V = \text{Change in volume of the system}$. Choose the correct answer from the options given below:

$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

Consider an engine that absorbs $130 \text{ cal}$ of heat from a hot reservoir and delivers $30 \text{ cal}$ of heat to a cold reservoir in each cycle. The engine also consumes $2 \text{ J}$ of energy in each cycle to overcome friction. If the engine works at $90 \text{ cycles per minute}$, what will be the maximum power delivered to the load (in $\text{ W}$)? [Assume the thermal equivalent of heat is $4.2 \text{ J/cal}$]