The initial pressure and volume of a gas are $P$ and $V$ respectively. First,the gas is expanded to a volume of $9V$ by an isothermal process,and then it is compressed to a volume of $V$ by an adiabatic process. What is its final pressure (in $P$)? (Ratio of specific heat at constant pressure to constant volume $\gamma = \frac{3}{2}$)

$A$ 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.............$J$.

Consider the thermodynamic cycle shown on the $PV$ diagram. The process $A \rightarrow B$ is isobaric,$B \rightarrow C$ is isochoric,and $C \rightarrow A$ is a straight-line process. The following internal energy change and heat are given: $\Delta U_{A \rightarrow B} = + 400 \text{ kJ}$ and $Q_{B \rightarrow C} = - 500 \text{ kJ}$. The heat flow in the process $Q_{C \rightarrow A}$ is ...... $\text{kJ}$.

For the $P-V$ diagram of a thermodynamic cycle as shown in the figure,processes $BC$ and $DA$ are isothermal. Which of the corresponding graphs is correct?

$A$ 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 engineer claims to have built an engine that delivers $10 \, kW$ of power with a fuel consumption of $1 \, g/s$. If the calorific value of the fuel is $2 \, kcal/g$, is the engineer's claim valid?