NSMQ Icon
NSMQ

Heat Engines, Entropy and the Second Law in Physics

The first law would allow any energy conversion you can imagine, as long as the books balance. The second law is what rules most of them out, and it does so with one blunt fact. Heat flows from hot to cold on its own and never the other way, so an engine can only turn part of the heat it receives into work, and the rest must be dumped somewhere colder. That waste is not a matter of bad engineering, it is written into the arithmetic, which is why the best possible engine between two temperatures depends only on those two temperatures. Entropy is the bookkeeping that measures how much of the energy has been spent, and the blocks finish with the statement that the total never falls.

Work output of a heat engine

Given

  • (J)
  • (J)
Thermal efficiency of a heat engine

Given

  • (J)
  • (J)
Coefficient of performance of a refrigerator

Given

  • (J)
  • (J)
Coefficient of performance of a heat pump

Given

  • (J)
  • (J)
Efficiency of a Carnot engine

Given

  • (K)
  • (K)
Coefficient of performance of a Carnot refrigerator

Given

  • (K)
  • (K)
Coefficient of performance of a Carnot heat pump

Given

  • (K)
  • (K)
Change in entropy in a general process

Given

  • (K)
  • (J)
Entropy change at a constant temperature

Given

  • (J)
  • (K)
Entropy change of a gas expanding at constant temperature

Given

  • (mol)
  • (m³)

Constant used

Entropy change of a body whose temperature changes

Given

  • (kg)
  • (J/(kg K))
  • (K)
Entropy change of a gas with both temperature and volume changing

Given

  • (mol)
  • (J/(mol K))
  • (K)
  • (m³)

Constant used

Entropy change during a change of state

Given

  • (kg)
  • (J/kg)
  • (K)
Second law of thermodynamics written with entropy

Given

  • (J/K)