QCC Notes
CLASS 11 · PHYSICSJEE MAIN × NEETहिंदी
§ 11.4NCERT Class 11 · Physics · Chapter 11

Second Law of Thermodynamics: Heat Engines & Refrigerators

QCC Notes · Class 11 Physics NCERT-aligned Updated 26 Sep 2026 5 min read

The First Law of Thermodynamics establishes the conservation of energy and states that ΔQ = ΔU + ΔW. However, it does not specify the direction in which thermodynamic processes can occur spontaneously. For example, the First Law would not be violated if heat flowed spontaneously from a colder body to a hotter body, or if a stone resting on the ground cooled down spontaneously and jumped into the air. The Second Law of Thermodynamics specifies this directional constraint and dictates the limits of energy conversion.

1. The Two Classical Statements of the Second Law

Kelvin-Planck Statement (Heat Engines)

"It is impossible to construct an engine operating in a cycle whose sole effect is to extract heat from a single thermal reservoir and convert it completely into an equivalent amount of mechanical work."

Physical Consequence: A heat engine must always reject a fraction of heat to a colder reservoir (sink). A 100% efficient heat engine (η = 1) is physically impossible.

Clausius Statement (Refrigerators)

"It is impossible to construct a cyclic device whose sole effect is the transfer of heat from a body at a lower temperature to a body at a higher temperature without the assistance of external work."

Physical Consequence: Spontaneous flow of heat from cold to hot never occurs; mechanical work input is mandatory to refrigerate a cold space.

Equivalence of Both Statements: A violation of the Kelvin-Planck statement leads directly to a violation of the Clausius statement, and vice versa. They are two equivalent formulations of the same fundamental law of nature.

2. Heat Engines

A heat engine is a cyclic thermodynamic device designed to convert thermal energy continuously into mechanical work. It consists of three essential components:

  1. Source (Hot Reservoir): A thermal reservoir of infinite heat capacity maintained at a constant high temperature T1.
  2. Working Substance: The medium (e.g., an ideal gas, steam, or fuel-air mixture) that absorbs heat, undergoes thermodynamic transformations, does work, and rejects leftover heat.
  3. Sink (Cold Reservoir): A thermal reservoir of infinite heat capacity maintained at a constant lower temperature T2 (where T2 < T1).

Energy Balance & Thermal Efficiency (η)

In one complete cycle, the working substance absorbs heat Q1 from the source at T1, performs net external mechanical work W, and rejects heat Q2 to the sink at T2. Since internal energy is a state function and the process is cyclic (ΔUcycle = 0):

W = Q1 − Q2

The thermal efficiency (η) of a heat engine is the ratio of net mechanical work output to total heat absorbed from the hot source:

η = W / Q1 = (Q1 − Q2) / Q1 = 1 − (Q2 / Q1)

Since Q2 > 0 according to the Kelvin-Planck statement, η < 1 (or η < 100%) for all physical engines.

3. Refrigerators & Heat Pumps

A refrigerator (or heat pump) is fundamentally a heat engine operating in the reverse direction. By performing external mechanical work W on the working substance, heat Q2 is extracted from a cold reservoir at temperature T2 and rejected as heat Q1 to a hotter reservoir at temperature T1.

Q1 = Q2 + W   ⇒   W = Q1 − Q2

Coefficient of Performance (COP, β) of a Refrigerator

The performance of a refrigerator is measured by its coefficient of performance (β), defined as the ratio of heat extracted from the cold refrigerated space (cooling effect Q2) to the external work input W required:

β = Q2 / W = Q2 / (Q1 − Q2)

Note: Unlike heat engine efficiency η which is strictly < 1, the COP β can be greater than 1 (typical household refrigerators have β ≈ 2 to 6).

Heat Pump COP (β')

When the purpose is to heat an interior room at temperature T1 by extracting heat from the cold exterior environment at T2, the device is called a heat pump. Its coefficient of performance (β') is defined by the heating delivered (Q1):

β' = Q1 / W = (Q2 + W) / W = 1 + β

4. Relationship between Engine Efficiency (η) & Refrigerator COP (β)

For two reversible systems operating between the same two thermal reservoirs:

β = Q2 / W = (Q1 − W) / W = (Q1 / W) − 1 = (1 / η) − 1 = (1 − η) / η
Exam Caution: If a refrigerator door is kept open in a closed, thermally insulated room, the temperature of the room will increase over time, because Q1 (heat released into the room) = Q2 + W > Q2 (heat extracted from inside the fridge). The net energy released into the room equals the electrical work W consumed by the motor.
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