$A$ 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)

$A$ Carnot cycle for a gas is represented in the pressure-volume $(P-V)$ diagram shown below. Consider the following statements:
$I.$ The area of $ABCD$ is the work done by the gas.
$II.$ The area of $ABCD$ is the total heat absorbed.
$III.$ The change in internal energy of the cycle is zero.
Which of the following is correct?

$10 \text{ mole}$ of oxygen is heated at constant volume from $30^{\circ} C$ to $40^{\circ} C$. The change in the internal energy of the gas is . . . . . . $\text{cal}$. (The molecular specific heat of oxygen at constant pressure, $C_p = 7 \text{ cal/mol}^{\circ} C$ and $R = 2 \text{ cal/mol}^{\circ} C$.)

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?
$(A)$ Process $I$ is an isochoric process
$(B)$ In process $II$,gas absorbs heat
$(C)$ In process $IV$,gas releases heat
$(D)$ Processes $I$ and $III$ are $not$ isobaric

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The process on the $P-V$ diagram is:

Consider an engine that absorbs $130 \text{ cal}$ of heat from a hot reservoir and delivers $30 \text{ cal}$ of heat to a cold reservoir in each cycle. The engine also consumes $2 \text{ J}$ of energy in each cycle to overcome friction. If the engine works at $90 \text{ cycles per minute}$, what will be the maximum power delivered to the load (in $\text{ W}$)? [Assume the thermal equivalent of heat is $4.2 \text{ J/cal}$]