Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A, B, C$ . Let $Q, W$ and $U$ represent the heat supplied to the gas, work done by the gas, and the internal energy of the gas, respectiely, then which of the following conditions is true?

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

The efficiency of a carnot engine is $0.6$.It rejects total $20 \ J$ of heat. The work done by the engine is   .... $J$

$P-V$ diagram of an ideal gas is as shown. Find work done by the gas in $ABCD$ process

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

A carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is $10 \;\mathrm{J},$ the amount of heat absorbed from the reservoir at lower temperature is .............. $\mathrm{J}$