A gas performs the maximum work, when it expands

To determine when a gas performs maximum work during expansion, let’s evaluate each process:

🔹 A. Non-uniformly
Usually implies irreversible or uncontrolled process.

Irreversible processes do not give maximum work.
❌ Incorrect

🔹 B. Adiabatically
No heat exchange.

Work is done at the expense of internal energy.

Compared to isothermal expansion, less work is done for the same volume change.
❌ Incorrect

🔹 C. Isobarically (constant pressure)
Work =
𝑊
=
𝑃
(
𝑉
2
−
𝑉
1
)
W=P(V
2
​
−V
1
​
)

Less work than isothermal expansion for an ideal gas under similar conditions.
❌ Incorrect

🔹 D. Isothermally (constant temperature)
For ideal gases, reversible isothermal expansion gives:

𝑊
=
𝑛
𝑅
𝑇
ln
⁡
(
𝑉
2
𝑉
1
)
W=nRTln(
V
1
​

V
2
​

​
)
This is the maximum possible work a gas can do between two volumes, since heat continuously enters to keep temperature constant and support expansion.

✅ Correct answer: D. Isothermally