Question

Which from following process involves zero work done?

• A. Isobaric expansion of gas.
• B. Adiabatic compression of gas.
• C. Isothermal expansion of gas.
• D. Free expansion of gas.

Hint:

Free Expansion = Expansion in Vacuum $\rightarrow P_{ext} = 0 \rightarrow W = 0$. No resistance, no work!

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In classical thermodynamics, pressure-volume work ($W$) done by or on a gaseous system is calculated based on the external pressure opposing the expansion or compression.
Step 2: Key Formula or Approach:
The general formula for irreversible pressure-volume work is: \[ W = -p_{\text{ext}} \Delta V \] where $p_{\text{ext}}$ is the external pressure and $\Delta V$ is the change in volume.
Step 3: Detailed Explanation:
Let's analyze the work done in each process described in the options: - (A) Isobaric expansion: This process occurs at a constant external pressure ($p_{\text{ext}}>0$). Since it is an expansion, $\Delta V>0$. Thus, the work done $W = -p_{\text{ext}} \Delta V$ is non-zero (specifically, work is done by the system). - (B) Adiabatic compression: This process involves a decrease in volume ($\Delta V<0$) against a positive external pressure. Thus, work done is non-zero (work is done on the system, raising its internal energy). - (C) Isothermal expansion: The gas expands against an external pressure while maintaining constant temperature. The work done is mathematically $W = -nRT \ln(V_f/V_i)$, which is non-zero. - (D) Free expansion: By definition, free expansion refers to the expansion of a gas into a vacuum. In a vacuum, there is no opposing force, so the external pressure is zero ($p_{\text{ext}} = 0$). Substituting this into the work equation gives $W = -0 \times \Delta V = 0$. Therefore, strictly zero work is done during free expansion.
Step 4: Final Answer:
Free expansion of gas involves zero work done.