One mole of an ideal gas $\left( {\frac{{{C_p}}}{{{C_v}}} = Y} \right)$ heated by law $P = \alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha $ is a constant. What is the molar heat capacity of gas in the process

- A
$C = \frac{R}{{\gamma - 1}}$

- B
$C = \frac{{\gamma R}}{{\gamma - 1}}$

- C
$C = \frac{R}{2}\frac{{\left( {\gamma - 1} \right)}}{{\left( {\gamma + 1} \right)}}$

- D
$C = \frac{R}{2}\frac{{\left( {\gamma + 1} \right)}}{{\left( {\gamma - 1} \right)}}$

In a Carnot engine, the temperature of reservoir is $927\ ^oC$ and that of sink is $27\ ^oC.$ If the work done by the engine is $12.6 \times 10^6 J,$ the quantitiy of heat absorbed by the engine from the reservoir is

$P-V$ diagram of $2\,g$ of $He$ gas for $A \to B$ process is shown. What is the heat given to the gas ?

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure

The change in internal energy of the gas during the transition is

If coefficient of performance of a refrigarator is $\beta $ and heat absorbed from refrigarated space is $Q$, then work done on the system is

In the following indicator diagram, the net amount of work done will be