Thermodynamics and Thermochemistry - Result Question 40
40. An ideal gas is expanded form $\left(p _1, V _1, T _1\right)$ to $\left(p _2, V _2, T _2\right)$ under different conditions. The correct statement(s) among the following is (are)
(2017 Adv.)
(a) The work done by the gas is less when it is expanded reversibly from $V_1$ to $V_2$ under adiabatic conditions as compared to that when expanded reversibly from $V_1$ to $V_2$ under isothermal conditions.
(b) The change in internal energy of the gas is (i) zero, if it is expanded reversibly with $T_1=T_2$, and (ii) zero, if it is expanded reversibly under adiabatic conditions with $T_1 \neq T_2$
(c) If the expansion is carried out freely, it is simultaneously neither isothermal nor adiabatic
(d) The work done on the gas is maximum when it is compressed reversibly from $\left(p _2, V _2\right)$ to $\left(p _1, V _1\right)$ against constant pressure $p _1$
Show Answer
Answer:
Correct Answer: 40. (a, c, d)
Solution:
Maximum work is done on the system when compression occurs irreversibly and minimum work is done in reversible compression.
(b)
$A B$ is isothermal and $A C$ is adiabatic path. Work done is area under the curve. Hence, less work is obtained in isothermal process than in adiabatic
(c) It is incorrect. In adiabatic expansion cooling is observed, hence $\Delta U=n C_v \Delta T < 0$.
(d) $q=0$ (adiabatic), $W=0$ (Free expansion)
Hence, $\Delta U=0, \Delta T=0$ (Isothermal process)
BETA
