Question

Which of the following statement(s) is/are correct?
[This question has multiple correct options]
(A) For same volume expansion, work done in reversible isothermal process is more as compared to reversible adiabatic process
(B) Reversible adiabatic process is also called isentropic process
(C) Free expansion is a reversible process
(D) If heat is given to a system, then its internal energy must change

Answer 1

Adiabatic process is a process in which the heat of the system remains constant over the period of the reaction. Free expansion is a process which is done in vacuum. Hence, their pressure is zero.

Complete Step-by-Step Solution:
We will check all the statements to check whether they are true or not.
A) We know that in adiabatic expansion, the heat of the system remains constant. So, pressure and temperature both decrease in the same volume expansion.
- Thus, the pressure is less in adiabatic process as compared to isothermal process. Thus, we know that work done is proportional to the pressure. So, we can say that the work done by adiabatic processes is less as compared to isothermal processes in a given case.
B) Isentropic process is a process in which the entropy remains constant throughout the reaction. All the reversible adiabatic processes are isentropic processes because entropy remains the same in the reactions.
C) Free expansion of a gas is the expansion of the gas in vacuum. So pressure is zero here. Free expansion is not just a reversible process. It can be irreversible also. So, the statement given in the option is not correct.
D) It is not correct in all the cases that internal energy always changes when heat is given to the system. When heat is given to the system, it may result in work and internal energy remains constant in isothermal processes. So, the statement given in the option is not correct.

- Thus, we can conclude that only options (A) and (B) are correct.

Note: The expression of the first law of thermodynamics is given as below.
$\Delta U = q + w$
Here, we can say that if heat is given to the system or taken out of the system, then its internal energy changes. But this is not seen in all of the cases. In isothermal processes, when heat is given to the system, it gets converted to work and internal energy of the system remains constant.