Question

The correct graphical depiction of the dependence of work done $\left(w\right)$ on the final volume $\left(V\right)$ in a closed system, with reversible isothermal expansion of an ideal gas at two different temperatures $T_{1}$ and $T_{2}\left(\right.T_{1} < T_{2}\left.\right)$

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

$w=-nRTln \left(\frac{v_{2}}{v_{1}}\right)$
$w=-nRTln \left(\frac{v_{f}}{v_{i}}\right)$
$\left|w\right|=nRT \, ln \frac{v_{b}}{v_{i}}$
$\left|w\right|=nRT\left(ln v_{f} - ln ⁡ v_{i}\right)$
$\left|w\right|=nRT \, ln v_{f}-nRTln ⁡ v_{i}$
$y=mx-c$
So for $\left(T_{2} > T_{1}\right)$ Intercept of $T_{2}$ would be more negative than $T_{1}$ and slope of curve $T_{2}$ would be more than slope of curve $\left(T_{1}\right)$ .