Q1. A heat engine takes 1000 J from a source and rejects 600 J to the sink. Find its efficiency.
η = 1 − Q₂/Q₁ = 1 − 600/1000
η = 1 − 0.6 = 0.4
η = 40%
Thermodynamics — Class 11
Heat and work are two sides of energy. Learn the laws of thermodynamics and compute the efficiency of an ideal heat engine.
Zeroth & first lawsZeroth: bodies in thermal equilibrium share a temperature. First: heat = change in internal energy + work done, Q = ΔU + W (energy conservation).
Thermodynamic processesIsothermal (constant T), adiabatic (no heat exchange), isobaric (constant P), isochoric (constant V).
Heat engineA device converting heat into work, taking heat Q₁ from a hot source and rejecting Q₂ to a cold sink; efficiency η = W/Q₁.
Carnot efficiencyThe maximum possible efficiency, η = 1 − T_cold/T_hot (temperatures in kelvin). No engine can beat it.
Carnot-efficiency calculator Interactive
Enter the source and sink temperatures (in kelvin) to get the maximum possible efficiency.
Max efficiency, 1 − T_c/T_h—%
Efficiency rises as the temperature difference grows; it can never reach 100% (that would need T_c = 0 K).
Numericals practice Interactive
Efficiency and first-law problems with steps.
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Solved numericals
Q2. In an adiabatic process, why does a gas cool when it expands?
Adiabatic means no heat is exchanged (Q = 0).
First law: 0 = ΔU + W, so ΔU = −W.
The gas does work by expanding, so its internal energy (and temperature) falls.
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| First law | Q = ΔU + W | joule (J) |
| Efficiency | η = W / Q₁ = 1 − Q₂/Q₁ | — |
| Carnot efficiency | η = 1 − T_c / T_h | — |
| Work (isobaric) | W = P ΔV | J |
Common mistakes & exam wins
- First law Q = ΔU + W is just conservation of energy for heat.
- Carnot efficiency uses ABSOLUTE (kelvin) temperatures — convert °C to K by adding 273.
- No real engine can exceed the Carnot efficiency between the same two temperatures.
- Isothermal ⇒ ΔU = 0 (Q = W); Adiabatic ⇒ Q = 0 (ΔU = −W).
Frequently asked questions
What is the first law of thermodynamics?
Heat supplied to a system equals the increase in its internal energy plus the work done by it: Q = ΔU + W (conservation of energy).
What is the efficiency of a Carnot engine?
η = 1 − T_c/T_h, the maximum efficiency possible between a hot source at T_h and a cold sink at T_c (in kelvin).
What is an adiabatic process?
A process in which no heat enters or leaves the system (Q = 0), so any work done changes the internal energy.