$A$ gas follows $VT^2 = \text{constant}$. The coefficient of volume expansion of the gas is

$A$ student records $\Delta Q, \Delta U,$ and $\Delta W$ for a thermodynamic cycle $A \rightarrow B \rightarrow C \rightarrow A$. Certain entries are missing in the table below. Find the correct entry from the following options.

	$AB$	$BC$	$CA$
$\Delta W$	$40 \, J$		$30 \, J$
$\Delta U$		$50 \, J$
$\Delta Q$	$150 \, J$	$10 \, J$

An ideal gas undergoes a cyclic process through various thermodynamic states. The heat energy $(Q)$ and work $(W)$ associated with these states are given as follows:
$Q_1 = 6000 \ J, Q_2 = -5500 \ J, Q_3 = -3300 \ J, Q_4 = 3500 \ J,$
$W_1 = 2500 \ J, W_2 = -1000 \ J, W_3 = -1200 \ J, W_4 = x \ J$
If the ratio of the net work done to the net heat absorbed is $\eta$, then the values of $x$ and $\eta$ are respectively:

$A$ sample of an ideal gas is taken through the cyclic process $ABCA$ as shown in the figure. It absorbs $40 \ J$ of heat during the part $AB$,no heat during $BC$,and rejects $60 \ J$ of heat during $CA$. $A$ work of $50 \ J$ is done on the gas during the part $BC$. The internal energy of the gas at $A$ is $1560 \ J$. The work done by the gas during the part $CA$ is.............$J$.

One mole of diatomic ideal gas undergoes a cyclic process $ABC$ as shown in the figure. The process $BC$ is adiabatic. The temperatures at $A, B$,and $C$ are $400\,K, 800\,K$,and $600\,K$ respectively. Choose the correct statement.

Match List-$I$ with List-$II$ :

List-$I$	List-$II$
$A$. Isothermal Process	$I$. Work done by the gas decreases internal energy
$B$. Adiabatic Process	$II$. No change in internal energy
$C$. Isochoric Process	$III$. The heat absorbed goes partly to increase internal energy and partly to do work
$D$. Isobaric Process	$IV$. No work is done on or by the gas

Choose the correct answer from the options given below :