Question

According to the second law, which of the following is impossible?

• A. Melting of ice at \( 0^\circ\text{C} \)
• B. \( 100\% \) conversion of heat to work
• C. Expansion of gas into a vacuum
• D. Reversible adiabatic expansion

Hint:

The Second Law essentially establishes that "you cannot break even." Some energy must always be degraded as low-grade heat during any cyclical conversion process.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks which physical process is prohibited by the Second Law of Thermodynamics.

Step 2: Key Formula or Approach:
The Kelvin-Planck statement of the Second Law states that it is impossible to construct a device that operates in a thermodynamic cycle and produces no other effect than the absorption of heat from a single reservoir and the performance of an equivalent amount of work.
Thus, the thermal efficiency (\( \eta \)) of any heat engine must satisfy:
\[ \eta = \frac{W_{\text{net}}}{Q_{\text{in}}} \lt 100\% \]

Step 3: Detailed Explanation:

• Impossibility of Complete Conversion: While work can be completely converted into heat (e.g., via friction), the reverse process—converting heat completely into work without any other change in the system or surroundings—is impossible in a thermodynamic cycle.
Some heat must always be rejected to a lower-temperature reservoir, meaning \( 100\% \) efficiency cannot be achieved.

• Validity of Other Options:
-

Melting of ice at \( 0^\circ\text{C} \) (Option A) is a naturally occurring phase transition at standard pressure.
-

Expansion of a gas into a vacuum (Option C) is a spontaneous process that increases the entropy of the universe, which is fully permitted by the second law.
-

Reversible adiabatic expansion (Option D) is an ideal, isentropic process that represents a theoretical limit, but is not fundamentally prohibited by thermodynamics.


Step 4: Final Answer:
Consequently, the \( 100\% \) conversion of heat to work is impossible, corresponding to Option (B).