Question

The figure shows a Carnot cycle for an ideal gas on a $P$ - $V$ diagram. Then (where $1$ - $2$ and $3$ - $4$ are isothermal and $2$ - $3$ and $4$ - $1$ are adiabatic process) (Note : $A_{2}$ and $A_{1}$ are the area bounded by curve $4 \rightarrow 1\&2 \rightarrow 3$ on $V$ -axis respectively.)

• A. $\frac{A_{1}}{A_{2}}=1$
• B. $\frac{A_{1}}{A_{2}}=2$
• C. $\frac{A_{1}}{A_{2}}=4$
• D. Data is insufficient

Answer 1

Answer: (A)

$2$ - $3$ and $4$ - $1$ are adiabatic processes and $1$ - $2$ and $3$ - $4$ are isothermal
$\therefore T_{1}=T_{2};T_{3}=T_{4}$
Work done in an adiabatic process depends on change in temperature. Change in temperature in both $2$ - $3$ and $4$ - $1$ is same.
$\therefore A_{1}=A_{2}$