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The First Law of Thermodynamics in Physics

The first law is conservation of energy written for systems that heat up, cool down, expand and get squeezed. It says that the internal energy of a gas can only change in two ways, by heat crossing the boundary or by work being done at the boundary, and nothing else counts. Every relation on this page is either a way of measuring one of those two transfers or a case where one of them is forced to zero. Fix the volume and no work is possible. Insulate the walls and no heat is possible. Complete a full cycle and the internal energy must come back to where it started. The blocks also cover the three ways heat travels, conduction, radiation, and the specific and latent heats that decide how much energy a temperature or a state change actually costs.

Heat needed to change the temperature of a body

Given

  • (kg)
  • (J/(kg K))
  • (K)
Heat needed using the heat capacity of the whole body

Given

  • (J/K)
  • (K)
Heat balance when two bodies are mixed

Given

  • (K)
  • (K)
Heat needed to change the state of a body

Given

  • (kg)
  • (J/kg)
Work done by a gas at constant pressure

Given

  • (Pa)
  • (m³)
Work done by a gas in a general process

Given

  • (m³)
Work done by a gas at constant volume

Given

  • (m³)
First law of thermodynamics

Given

  • (J)
  • (J)
First law for an adiabatic process

Given

  • (J)
First law for a process at constant volume

Given

  • (J)
First law for a complete cycle

Given

  • (J)
  • (J)
Heat added at constant volume for an ideal gas

Given

  • (mol)
  • (J/(mol K))
  • (K)
Heat added at constant pressure for an ideal gas

Given

  • (mol)
  • (J/(mol K))
  • (K)
Difference between the molar specific heats of an ideal gas

Given

  • (J/(mol K))
  • (J/(mol K))

Constant used

Rate of heat conduction through a slab

Given

  • (W/(m K))
  • (m²)
  • (K)
  • (m)
Thermal resistance of a slab

Given

  • (m)
  • (W/(m K))
  • (m²)
Rate at which a hot body radiates energy

Given

  • (m²)
  • (K)

Constant used

Net rate of energy radiated by a body in cooler surroundings

Given

  • (m²)
  • (K)
  • (K)

Constant used