Question

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process \((ab)\), followed by an isochoric process \((bc)\) and an adiabatic process \((ca)\) as shown in the figure. The volumes of the gas are \(V_1\) and \(V_2\) at \(a\) and \(b\), respectively. If the cycle has heat input \(Q_{\mathrm{in}}\) and output \(Q_{\mathrm{out}}\), then the efficiency of the cycle is defined as \[ \eta=\frac{Q_{\mathrm{in}}-Q_{\mathrm{out}}}{Q_{\mathrm{in}}} \] The correct statement(s) is/are: \[ [\text{Given: }\ln2\approx0.7] \]

• A. If \(\dfrac{V_2}{V_1}=8\), the heat released in process \(bc\) is smaller than the heat absorbed in process \(ab\)
• B. For a given value of \(\dfrac{V_2}{V_1}\), \(\eta\) does not depend on the temperature of the isothermal process
• C. If \(\dfrac{V_2}{V_1}=8\), then temperature at \(a\) is \(4\) times temperature at \(c\)
• D. If \(\dfrac{V_2}{V_1}=8\), then pressure at \(a\) is \(4\) times pressure at \(b\)

Hint:

For adiabatic process: \[ TV^{\gamma-1}=\text{constant} \] For isothermal process: \[ PV=\text{constant} \]

Answer 1

The Correct Option is A