Which of the following is correct in terms of increasing work done for the same initial and final state?

  • A
    Adiabatic < Isothermal < Isobaric
  • B
    Isobaric < Adiabatic < Isothermal
  • C
    Adiabatic < Isobaric < Isothermal
  • D
    None of these

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$n$ moles of a perfect gas undergo a cyclic process $ABCA$ (see figure) consisting of the following processes:
$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V_{1}$ to $V_{2}=2V_{1}$ and pressure changes from $P_{1}$ to $P_{2}$.
$B \rightarrow C :$ Isobaric compression at pressure $P_{2}$ to initial volume $V_{1}$.
$C \rightarrow A :$ Isochoric change leading to a change of pressure from $P_{2}$ to $P_{1}$.
Total work done in the complete cycle $ABCA$ is

$A$ gas obeying the equation of state $pV = RT$ undergoes a hypothetical reversible process described by the equation $pV^{5/3} \exp \left(-\frac{pV}{E_0}\right) = C_1$,where $C_1$ and $E_0$ are dimensioned constants. Then,for this process,the thermal compressibility at high temperature

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Column-$I$ Column-$II$
$(a)$ Heat engine $(i)$ $\eta = \frac{Q_2}{Q_1 - Q_2}$
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$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

Two moles of monoatomic gas is expanded from $(P_0, V_0)$ to $(P_0, 2V_0)$ under isobaric condition. Let $\Delta Q_1$,$\Delta W_1$,and $\Delta U_1$ be the heat given to the gas,the work done by the gas,and the change in internal energy,respectively. Now,the monoatomic gas is replaced by a diatomic gas,with other conditions remaining the same. The corresponding values in this case are $\Delta Q_2$,$\Delta W_2$,and $\Delta U_2$. Then:

In changing the state of a gas adiabatically from an equilibrium state $A$ to another equilibrium state $B$,an amount of work equal to $22.3 \; J$ is done on the system. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $9.35 \; cal$,how much is the net work done (in $J$) by the system in the latter case? (Take $1 \; cal = 4.19 \; J$)

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