Example 1: Heat Engine
A steam power plant takes in heat from a boiler at 500°C and rejects heat to a condenser at 30°C. According to Kelvin–Planck, it cannot convert all the boiler heat into work; some must be rejected to the condenser.
1) Introduction
The Second Law of Thermodynamics introduces the concept of directionality and feasibility of processes, complementing the First Law (energy conservation). It tells us which processes can occur spontaneously and sets limits on the conversion of heat into work.
2) Why the Second Law is Needed
- The First Law states that energy is conserved, but does not indicate the direction of processes.
- It cannot explain why certain energy conversions are impossible (e.g., complete conversion of heat into work in a cycle).
- The Second Law addresses these limitations by introducing constraints based on natural irreversibility.
3) Kelvin–Planck Statement
Statement: “It is impossible to construct a device that operates in a cycle and produces no effect other than the extraction of heat from a single thermal reservoir and the performance of an equivalent amount of work.”
Meaning: No heat engine can have 100% thermal efficiency when operating between a single reservoir and producing only work. There must be heat rejection to a lower-temperature reservoir.
Implication: All practical heat engines must reject some heat; efficiency is always less than 1.
4) Clausius Statement
Statement: “It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a colder body to a hotter body without the input of external work.”
Meaning: Heat cannot spontaneously flow from cold to hot; to do so requires work input (as in refrigerators and heat pumps).
Implication: Refrigerators and heat pumps must consume work to move heat against the natural temperature gradient.
5) Equivalence of the Statements
- Though worded differently, the Kelvin–Planck and Clausius statements are equivalent.
- Proof of equivalence: A violation of one statement would allow construction of a device that violates the other, using reversible cycles as intermediaries.
- Both forbid perpetual motion machines of the second kind (PMM2).
6) Implications for Engineering
- Sets the upper limit for efficiency of heat engines (Carnot efficiency).
- Defines the need for work input in refrigeration and heat pump cycles.
- Forms the basis for the concept of entropy and the Clausius inequality.
- Guides design toward minimizing irreversibilities to approach ideal performance.
7) Illustrative Examples
Example 2: Refrigerator
A domestic refrigerator moves heat from the cold interior to the warmer kitchen air. According to Clausius, this requires electrical work input to the compressor.
8) Common Misconceptions
- Believing that the Second Law forbids any conversion of heat to work — it forbids complete conversion in a cycle without other effects.
- Thinking that heat cannot flow from cold to hot under any circumstances — it can, but only with work input.
- Assuming the statements are unrelated — they are logically equivalent.
9) Summary Checklist
- Kelvin–Planck: No cyclic device can convert heat from a single reservoir entirely into work.
- Clausius: No cyclic device can transfer heat from cold to hot without work input.
- Both statements are equivalent and forbid PMM2.
- They set fundamental limits on heat engine and refrigeration performance.