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: A2 and A1 are the area bounded by curve 4 arrow 1 &2 arrow 3 on V -axis respectively.)

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: A2 and A1 are the area bounded by curve 4 arrow 1 &2 arrow 3 on V -axis respectively.) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-nprtiufj4dcdfl56.jpg" /> (A) (A1/A2)=1 (B) (A1/A2)=2 (C) (A1/A2)=4 (D) Data is insufficient

Tardigrade Admin · Accepted Answer

2 - 3 and 4 - 1 are adiabatic processes and 1 - 2 and 3 - 4 are isothermal ∴ T1=T2;T3=T4 Work done in an adiabatic process depends on change in temperature. Change in temperature in both 2 - 3 and 4 - 1 is same. ∴ A1=A2

Q. 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 $4 \to 1&2 \to 3$ on $V$ -axis respectively.)

$\frac{A _{1}}{A _{2}} = 1$

$\frac{A _{1}}{A _{2}} = 2$

$\frac{A _{1}}{A _{2}} = 4$

Data is insufficient

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

Q. 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 : A2​ and A1​ are the area bounded by curve 4→1&2→3 on V -axis respectively.)

A2​A1​​=1

A2​A1​​=2

A2​A1​​=4