Thermodynamics and Thermochemistry - Result Question 44
44. The reversible expansion ob an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?
(2012)
(a) $T _1=T _2$
(b) $T _3>T _1$
(c) $W _{\text {isothermal }}>W _{\text {adiabatic }}$
(d) $\Delta U _{\text {isothermal }}>\Delta U _{\text {adiabatic }}$
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Answer:
Correct Answer: 44. (a, c, d)
Solution:
(a) Since, change of state $\left(p _1, V _1, T _1\right)$ to $\left(p _2, V _2, T _2\right)$ is isothermal therefore, $T _1=T _2$.
(b) Since, change of state $\left(p _1, V _1, T _1\right)$ to $\left(p _3, V _3, T _3\right)$ is an adiabatic expansion it brings about cooling of gas, therefore, $T _3 < T _1$.
(c) Work done is the area under the curve of $p-V$ diagram. As obvious from the given diagram, magnitude of area under the isothermal curve is greater than the same under adiabatic curve, hence $W _{\text {isothermal }}>W _{\text {adiabatic }}$
(d) $\Delta U=n C _v \Delta T$
In isothermal process, $\Delta U=0$ as $\Delta T=0$
In adiabatic process, $\Delta U=n C _v\left(T _3-T _1\right) < 0$ as $T _3 < T _1$.
$ \Rightarrow \quad \Delta U _{\text {isothermal }} > \Delta U _{\text {adiabatic }} $
NOTE: Here only magnitudes of work is being considered otherwise both works have negative sign.
BETA
