$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$. The vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings,the temperature of the gas increases by ... ($R =$ universal gas constant)

In the given $P-V$ diagram,a monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5, \ln 2 \simeq 0.7$].
Which of the following statement$(s)$ is(are) correct?
$(A)$ The magnitude of the total work done in the process $A \rightarrow B \rightarrow C$ is $144 \text{ kJ}$.
$(B)$ The magnitude of the work done in the process $B \rightarrow C$ is $84 \text{ kJ}$.
$(C)$ The magnitude of the work done in the process $A \rightarrow B$ is $60 \text{ kJ}$.
$(D)$ The magnitude of the work done in the process $C \rightarrow A$ is zero.

Two gases have the same initial pressure,volume,and temperature. They expand to the same final volume,one adiabatically and the other isothermally.

Match the following lists.

List-$I$	List-$II$
$A$. Zeroth law of thermodynamics	$I$. Direction of flow of heat
$B$. First law of thermodynamics	$II$. Work done is zero
$C$. Free expansion of a gas	$III$. Thermal equilibrium
$D$. Second law of thermodynamics	$IV$. Law of conservation of energy

The correct answer is:

Which of the following statements is incorrect?

One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).