Question

Which of the following processes produces maximum work?

• A. Rapid expansion of gas
• B. Free expansion
• C. Reversible expansion
• D. Irreversible expansion

Hint:

Maximum work is always associated with reversible paths in thermodynamics.
Minimum work input (for compression) is also achieved via a reversible path.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks which thermodynamic process yields the maximum work output during the expansion of a gas.

Step 2: Key Formula or Approach:
Work done during the expansion of a gas is given by:
\[ W = \int P_{\text{ext}} dV \]
where $P_{\text{ext}}$ is the external pressure opposing the expansion.

Step 3: Detailed Explanation:

• Reversible Expansion: In a reversible process, the expansion occurs infinitely slowly such that the system is always in thermodynamic equilibrium with its surroundings. Under these conditions, the opposing external pressure is only infinitesimally smaller than the gas pressure ($P_{\text{ext}} = P_{\text{sys}} - dP$). This maximizes the value of $P_{\text{ext}}$ at every step of the integration, producing the maximum possible work output.

• Irreversible Rapid Expansion: In any real, irreversible expansion, the external pressure is significantly lower than the system's pressure, which leads to lower work output due to frictional and dissipative losses.

• Free Expansion: In a free expansion, a gas expands into a vacuum where $P_{\text{ext}} = 0$. Consequently, the work done is exactly zero ($W = 0$).

Step 4: Final Answer:
The process that produces maximum work is reversible expansion.