Question

An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are $Q_1=5960\text{J}$, $Q_2=-5585\text{J}$, $Q_3=-2980\text{J}$ and $Q_4=3645\text{J}$ respectively. The corresponding quantities of work involved are $W_1=2200\text{J}$, $W_2=-825\text{J},W_3=-1100\text{J}$ and $W_4$ respectively . Find the efficiency of the cycle.

• A. $10.82\%$
• B. $17.44\%$
• C. $28.53\%$
• D. $30.86\%$

Answer 1

The correct option is A $10.82\%$

For a cyclic process, since the initial and final states are same, we can say that, $\Delta U=0$
$\therefore$ By using first law of thermodynamics, we get
$\Delta Q=\Delta W$
i.e Net work done $W_{net}=Q_1+Q_2+Q_3+Q_4$
$=1040\text{J}$ [using the data given in the question]

Efficiency of the cyclic process$\eta =\frac{\text{Net work done}}{\text{Total heat supplied}}=\frac{W_{net}}{Q_1+Q_4}$
$=\frac{1040}{9605}=0.1082$ or $10.82$%
Thus, option (a) is the correct answer.