Clausius Statement of second law states that a heat engine cannot operate in a cycle by exchanging heat with only one heat source: (a) True(b) False
The correct answer and explanation is:
Correct Answer: (a) True
Explanation:
The Clausius Statement of the Second Law of Thermodynamics states:
“It is impossible for a self-acting machine, unaided by any external agency, to transfer heat from a colder body to a hotter body.”
However, your question relates more closely to the Kelvin-Planck Statement, which is often confused with Clausius’s. The Kelvin-Planck Statement is:
“It is impossible to construct a heat engine that operates on a cycle and produces no effect other than the absorption of heat from a single reservoir and the performance of an equal amount of work.”
In other words, a heat engine cannot operate in a cycle by exchanging heat with only one heat reservoir (source). This is the essence of your question, and it is true.
Why is this True?
For a heat engine to perform work, it must absorb heat from a high-temperature reservoir and reject some of that heat to a low-temperature reservoir. This is because:
- Energy Conversion Requires a Gradient: Work can only be extracted when there is a temperature difference—much like water can only do work as it flows from a high point to a low point. Without a cold reservoir, there’s nowhere for the rejected heat to go.
- Violation of Second Law: If a heat engine could operate by absorbing heat from a single reservoir and converting it all into work with no heat rejection, it would violate the second law by being 100% efficient—something that is thermodynamically impossible.
Conclusion:
The statement is True. A heat engine must interact with at least two reservoirs—one hot (to absorb heat) and one cold (to reject waste heat)—to continuously perform work in a cyclic process. This fundamental principle upholds the second law of thermodynamics.