When $Q_1$ amount of heat is supplied to a monatomic gas,the work done by the gas is $W$. When $Q_2$ amount of heat is supplied to a diatomic gas,the work done by the gas is $2W$. Then $Q_1: Q_2=$

$A$ monoatomic gas of pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (ratio of specific heats $\gamma = \frac{5}{3}$)

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \rightarrow 2$ takes place at a constant temperature $(300 \ K)$. Process $2 \rightarrow 3$ takes place at a constant volume. During this process,$40 \ J$ of heat leaves the system. Process $3 \rightarrow 1$ is adiabatic and the temperature $T_3$ is $275 \ K$. The work done by the gas during the process $3 \rightarrow 1$ is ..... $J$.

$A$ cyclic process $ABCD$ is shown in the $p-V$ diagram. Which of the following curves represents the same process if $BC$ and $DA$ are isothermal processes?

$A$ given amount of gas has an initial state $(P_i, V_i, T_i)$. It expands until its volume becomes $V_f$. Consider the following two cases:
$(a)$ The expansion occurs at constant temperature (isothermal).
$(b)$ The expansion occurs at constant pressure (isobaric).
Draw the $P-V$ diagram for each case. In which of the two cases is the work done by the gas greater?

Thermodynamic processes are indicated in the following diagram. Match the following:

Column-$1$	Column-$2$
$P$: Process-$I$	$A$: Adiabatic
$Q$: Process-$II$	$B$: Isobaric
$R$: Process-$III$	$C$: Isochoric
$S$: Process-$IV$	$D$: Isothermal