Question

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is(are) correct?

[This question has multiple correct options]
(A) $T_1=T_2$
(B) $T_3>T_1$
(C) $w_{isothermal}>w_{adiabatic}$
(D) $\mathrm{\Delta }{U}_{isothermal}>\mathrm{\Delta }{U}_{adiabatic}$

Answer 1

Hint: Isothermal process is a process in which the temperature remains the same throughout the process. So, $\mathrm{\Delta }T=0$. In adiabatic processes, the heat of the system remains constant, so $\mathrm{\Delta }Q=0$ .

Complete answer:
We will find which of the statements are wrong as given in the graph.
- Isothermal process is a process in which the temperature remains the same throughout the process. In the isothermal curve, we can see that the initial temperature is $T_1$ and the final temperature is $T_2$. We know that as the process is isothermal, the temperature will not change. Thus, we can say that $T_1=T_2$.
- In adiabatic processes, the heat of the system remains constant. So, in this process, we can say that the initial temperature is shown as $T_1$ in the adiabatic curve. The final temperature is $T_3$. We can say that the final temperature is lower than the initial temperature from the curve. Thus, $T_1>T_3$.
- In the isothermal process, we know that $\mathrm{\Delta }{U}_{isothermal}$ is zero. Thus, we can say that this energy gets converted into work ($w_{isothermal}$) done. For adiabatic process, Q = 0. Thus, we can say that the work done by the isothermal process will be higher than the adiabatic process. So, $w_{isothermal}>w_{adiabatic}$
- We have seen earlier that the change in internal energy in isothermal energy is zero. Thus, $\mathrm{\Delta }{U}_{isothermal}=0$ . But in adiabatic processes, the work done is always negative. So, we can say that $\mathrm{\Delta }{U}_{isothermal}>\mathrm{\Delta }{U}_{adiabatic}$

Thus, we can conclude that options (A), (C) and (D) are correct.

Note:
Remember that a process can be called reversible if the change is brought in such a way that it can be reversed by a change. It involves equilibrium states in it. The processes that are not reversible are called irreversible processes.