Question

Which of the following are correct about irreversible isothermal expansion of ideal gas?
(A) $w=-q$
(B) $\Delta U=0$
(C) $\Delta T=0$
(D) $w=-nRT\ln \dfrac{{{P}_{1}}}{{{P}_{2}}}$

Answer 1

Hint: Recollect the First Law of Thermodynamics which states, ‘The sum of the mass and the total internal energy of an isolated system is constant’. The question says, for an ‘isothermal expansion’ which means work is done on the system by the surroundings when the temperature is constant.

Complete answer:
In the question, it is mentioned ‘for an Irreversible Isothermal ideal gas’. Let’s discuss what it means.
-Irreversible means once the work is done on the system by the surroundings, it cannot be reversed to the initial state.
-Isothermal means at constant temperature. When temperature is constant, $\Delta T=0$.
-When the temperature is constant, there is no change in the internal energy of the system. Therefore, $\Delta U=0$
-According to First Law of Thermodynamics, ‘When work is done on the system, the total internal energy of the system and the surroundings remains the same’.
-Mathematically, it can be represented as,
\[\Delta U=q+W\]
where $\Delta U$= change in internal energy of the system, q = heat supplied to the system and W= Work done
-In this case, $\Delta U=0$ and therefore,
\[0=q+W\]
\[W=-q\]

Therefore, the correct options are (A) $w=-q$, (B) $\Delta U=0$ and (C) $\Delta T=0$.

Additional Information:
Let’s see why option (D) is incorrect. The equation, $w=-nRT\ln \dfrac{{{P}_{1}}}{{{P}_{2}}}$represents the expression for maximum work done, ${{W}_{\max }}$ for a ‘Reversible’ isothermal expansion of an ideal gas.

Note:
It is important to read what is asked in the question. Learn to read in between the lines because most of the time the answer is in the question itself. Please don’t get confused with the reversible isothermal expansion and irreversible isothermal expansion. If the question just mentions, “isothermal expansion” then it is to be understood that irreversible work is done on the system. Unless explicitly specified that work done is “Reversible”, assume that work done on the system is irreversible.