Question

On a TP diagram, two moles of ideal gas perform process AB and CD. If the work done by the gas in the process AB is two times the work done in the process CD then what is the value of $T_1/T_2$?

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (A)

$\frac{1}{2}$

Work done in Isothermal process

$W=nRT\ell n\frac{P_1}{P_2}⟶\left(1\right)$

$\therefore W_{AB}=2R{T}_1\ell n\frac{P_A}{P_B}$

$\Rightarrow W_{CD}=2R{T}_2\ell n\frac{P_C}{P_D}$

$T$ varies proportionally to $P$

$\frac{P_A}{P_B}=\frac{P_C}{P_D}⟶\left(2\right)$

$\Rightarrow W_{AB}=2W_{CD}$

$\Rightarrow \frac{W_{AB}}{W_{CD}}=\frac{T_1}{T_2}={\left(\frac{1}{2}\right)}^{-1}$

$\Rightarrow \frac{T_2}{T_1}=\frac{1}{2}.$

Hence, the answer is $\frac{1}{2}.$