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

$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$,respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure,the pistons of gas $A$ and $B$ are displaced by $16 \ cm$ and $9 \ cm$,respectively. If the change in their internal energy is the same,then the ratio $\frac{r_A}{r_B}$ is equal to

One mole of a diatomic ideal gas undergoes a process shown in $P-V$ diagram. The total heat given to the gas $(\ln 2 = 0.7)$ is (in $P_0 V_0$)

Consider two containers $A$ and $B$ containing identical gases at the same pressure,volume and temperature. The gas in container $A$ is compressed to half of its original volume isothermally while the gas in container $B$ is compressed to half of its original volume adiabatically. The ratio of final pressure of gas in $B$ to that of gas in $A$ is

When a system is taken from a state $i$ to $f$ along the path $iaf$ (as shown in the figure),$Q = 50 \, cal$ and $W = 20 \, cal$. Along path $ibf$,$Q = 36 \, cal$.
$(i)$ What is $W$ along path $ibf$?
$(ii)$ If $W = -13 \, cal$ for path $fi$,what is $Q$ for the path $fi$?
$(iii)$ Take $E_{int,i} = 10 \, cal$,then what is $E_{int,f}$?