Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the change in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from $T_1$ to $T_2$ is proportional to $(T_2 - T_1)$.
Choose the correct answer from the options given below:
Answer: (C) (B), (E) only
In an adiabatic process $Q = 0$, so $W = -\Delta U$: the work done equals the change in internal energy in magnitude, so (B) holds and (A) is false (temperature changes, so $U$ changes).
$|W| = nC_V|T_2 - T_1|$, which is proportional to $(T_2 - T_1)$, so (E) holds.
For a monoatomic gas the adiabatic relations are $TV^{2/3} = \text{constant}$ and $PV^{5/3} = \text{constant}$, so neither $TV$ nor $PV$ is constant: (C) and (D) are false.
Answer: (B) and (E) only.
Solution by Sreeraj P, M.Sc Physics