Second Law, Heat Engines and Refrigerators
Reversible and irreversible processes, efficiency and coefficient of performance. (Physics › Thermodynamics, NEET UG syllabus.)
What is Second Law, Heat Engines and Refrigerators?
States that heat cannot spontaneously flow from a colder body to a hotter body, and it's impossible to convert all absorbed heat into work in a cyclic process.
Key formula / rule: Efficiency of a general heat engine
Key points
- State the Kelvin-Planck and Clausius statements of the Second Law of Thermodynamics.
- Explain the working principle of a heat engine and calculate its efficiency.
- Describe the Carnot cycle and calculate the efficiency of a Carnot engine.
- Explain the working principle of a refrigerator and a heat pump and calculate their Coefficients of Performance.
Common exam trap
Using Celsius instead of Kelvin for temperature in efficiency/COP calculations.
Definitions
- Term
Second Law of Thermodynamics
- Meaning
States that heat cannot spontaneously flow from a colder body to a hotter body, and it's impossible to convert all absorbed heat into work in a cyclic process.
- Term
Heat Engine
- Meaning
A device that converts thermal energy into mechanical work by operating in a cycle between a high-temperature source and a low-temperature sink.
- Term
Efficiency (η)
- Meaning
The ratio of the net work done by a heat engine to the heat absorbed from the high-temperature source.
- Term
Carnot Engine
- Meaning
An ideal, reversible heat engine operating on the Carnot cycle, which has the maximum possible efficiency between two given temperatures.
- Term
Refrigerator
- Meaning
A device that transfers heat from a colder reservoir to a hotter reservoir, requiring external work input, primarily for cooling purposes.
- Term
Heat Pump
- Meaning
A device that transfers heat from a colder reservoir to a hotter reservoir, requiring external work input, primarily for heating purposes.
- Term
Coefficient of Performance (COP)
- Meaning
A measure of the effectiveness of a refrigerator or heat pump, defined as the ratio of the desired heat transfer to the work input.
- Term
Source (High-Temperature Reservoir)
- Meaning
The reservoir from which a heat engine absorbs heat or to which a heat pump/refrigerator rejects heat; characterized by temperature T₁.
- Term
Sink (Low-Temperature Reservoir)
- Meaning
The reservoir to which a heat engine rejects heat or from which a heat pump/refrigerator absorbs heat; characterized by temperature T₂.
- Term
Reversible Process
- Meaning
An idealized process that can be reversed without leaving any change in the surroundings or the system.
- Term
Irreversible Process
- Meaning
A process that cannot be reversed without leaving some change in the surroundings; all natural processes are irreversible.
Learning objectives
State the Kelvin-Planck and Clausius statements of the Second Law of Thermodynamics.
Explain the working principle of a heat engine and calculate its efficiency.
Describe the Carnot cycle and calculate the efficiency of a Carnot engine.
Explain the working principle of a refrigerator and a heat pump and calculate their Coefficients of Performance.
Differentiate between reversible and irreversible processes.
Apply the Second Law to real-world scenarios involving heat transfer and energy conversion.
Formulae
- Name
Efficiency of a general heat engine
- Note
W is work done, Q₁ is heat absorbed from source, Q₂ is heat rejected to sink.
- Expression
η = W/Q₁ = (Q₁ - Q₂)/Q₁ = 1 - Q₂/Q₁
- Name
Efficiency of a Carnot (reversible) engine
- Note
T₁ is absolute temperature of source, T₂ is absolute temperature of sink (in Kelvin).
- Expression
ηCarnot = 1 - T₂/T₁
- Name
Coefficient of Performance (COP) of a refrigerator
- Note
Q₂ is heat extracted from cold reservoir, W is work input, Q₁ is heat rejected to hot reservoir.
- Expression
COPref = Q₂/W = Q₂/(Q₁ - Q₂)
- Name
COP of a reversible refrigerator
- Note
T₁ is absolute temperature of hot reservoir, T₂ is absolute temperature of cold reservoir (in Kelvin).
- Expression
COPref = T₂/(T₁ - T₂)
- Name
Coefficient of Performance (COP) of a heat pump
- Note
Q₁ is heat delivered to hot reservoir, W is work input, Q₂ is heat extracted from cold reservoir.
- Expression
COPHP = Q₁/W = Q₁/(Q₁ - Q₂)
- Name
COP of a reversible heat pump
- Note
T₁ is absolute temperature of hot reservoir, T₂ is absolute temperature of cold reservoir (in Kelvin).
- Expression
COPHP = T₁/(T₁ - T₂)
- Name
Relationship between COPHP and COPref
- Note
Applies to both general and reversible devices operating between the same two reservoirs.
- Expression
COPHP = COPref + 1
Prerequisites
First Law of Thermodynamics (conservation of energy).
Concepts of heat, work, and internal energy.
Understanding of thermodynamic processes (isothermal, adiabatic, isobaric, isochoric).
Basic knowledge of ideal gas laws.
Familiarity with temperature scales (Celsius, Kelvin).
Common mistakes
Using Celsius instead of Kelvin for temperature in efficiency/COP calculations.
Confusing Q₁ (heat absorbed from source) and Q₂ (heat rejected to sink).
Mixing up efficiency (η) for engines and Coefficient of Performance (COP) for refrigerators/heat pumps.
Assuming COP is always less than 1.
Not understanding the distinct objectives of a heat engine (produce work), refrigerator (cool cold space), and heat pump (heat warm space).
Forgetting that W = Q₁ - Q₂ (magnitude of work done) applies to both engines and refrigerators/heat pumps.
Applying Carnot efficiency/COP formulas to non-Carnot (irreversible) engines/devices.
Keywords
Second Law of Thermodynamics
Kelvin-Planck statement
Clausius statement
Heat Engine
Efficiency
Carnot Engine
Carnot Cycle
Refrigerator
Heat Pump
Coefficient of Performance (COP)
Source
Sink
Reversible process
Irreversible process
Absolute temperature
Practice preview
The efficiency of a heat engine is defined as the ratio of:…
easy
A Carnot engine operates between a source at 500 K and a sink at 300 K. What is its thermal efficiency?…
medium
A refrigerator has a coefficient of performance of 5. If it rejects 120 J of heat to the surroundings in one cycle, how much heat is absorbed from the cold reservoir?…
medium