Thermodynamics and Thermochemistry 1 Question 37
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 form $V_{1}$ 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) positive, 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 both isothermal as well as adiabatic
(d) The work done on the gas is maximum when it is compressed irrversibly from $\left(p_{2}, V_{2}\right)$ to $\left(p_{1}, V_{1}\right)$ against constant pressure $p_{1}$
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Solution:
(a)
Irreversible compression
Reversible compression
Maximum work is done on the system when compression occur irreversibly and minimum work is done is 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 adiabatic process than in isothermal
(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)
