The amount of work,which can be obtained by supplying $200 \, cal$ of heat,is

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \rightarrow 2$ takes place at a constant temperature $(300 \ K)$. Process $2 \rightarrow 3$ takes place at a constant volume. During this process,$40 \ J$ of heat leaves the system. Process $3 \rightarrow 1$ is adiabatic and the temperature $T_3$ is $275 \ K$. The work done by the gas during the process $3 \rightarrow 1$ is ..... $J$.

Three moles of an ideal gas $\left( {{C_P} = \frac{7}{2}R} \right)$ at pressure ${P_A}$ and temperature ${T_A}$ is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally, the gas is compressed at constant volume to its original pressure ${P_A}.$ The correct $P-V$ and $P-T$ diagrams indicating the process are

Match the "Technology" given in List-$1$ with the "Principle of Physics" given in List-$2$.

$A$. Steam engine	$I$. Magnetic confinement of plasma
$B$. Electron microscope	$II$. Laws of thermodynamics
$C$. Non-reflecting coatings	$III$. Wave nature of electrons
$D$. Tokamak	$IV$. Interference of light

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

$A$ thermodynamic system goes from states $(i) \, P_1, V$ to $2P_1, V$ and $(ii) \, P, V$ to $P, 2V$. The work done in the two cases is: