JEE PYQ: Thermodynamics Question 30
Question 30 - 2019 (09 Jan Shift 1)
Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $T_1$ and $T_2$ ($T_1 < T_2$). The correct graphical depiction of the dependence of work done ($w$) on the final volume ($V$) is:
(1) Graph shows $|w|$ vs $\ln V$ with two straight lines from origin, $T_2$ having greater slope than $T_1$
(2) Graph shows $|w|$ vs $\ln V$ with two curves, $T_2$ above $T_1$
(3) Graph shows $|w|$ vs $\ln V$ with two curves, $T_2$ above $T_1$, both curving upward
(4) Graph shows $|w|$ vs $\ln V$ with two straight lines from origin, $T_1$ having greater slope than $T_2$
Show Answer
Answer: (2)
Solution
$w = -nRT\ln\dfrac{V_2}{V_1}$. $|w| = nRT\ln\dfrac{V_2}{V_1} = nRT(\ln V_2 - \ln V_1)$. $|w| = nRT\ln V_2 - nRT\ln V_1$, which is of the form $y = mx + c$. So, slope of curve 2 ($T_2$) is more than curve 1 ($T_1$) and intercept of curve 2 is more negative than curve 1.
BETA
