Physics formulas: Thermodynamics

Quick reference for school physics (thermodynamics). Browse by topic or search by name.

Thermodynamics

Internal energy of an ideal gas

U=i2 nRTU = \frac{i}{2}\, nRT
Symbols
  • UU — internal energy of the ideal gas, J (joule)
  • ii — number of degrees of freedom, dimensionless quantity
  • nn — amount of substance (moles), mol
  • RR — universal gas constant, 8.31 J/(mol·K)
  • TT — absolute temperature, K (kelvin)
For a monatomic gas i=3i = 3, so U=32 nRTU = \frac{3}{2}\, nRT.
Thermodynamics

Heat absorbed or released when temperature changes

Q=cmΔtQ = cm\Delta t
Symbols
  • QQ — heat transferred, J (joule)
  • cc — specific heat capacity, J/(kg·K)
  • mm — mass of the body, kg (kilogram)
  • Δt\Delta t — change in temperature, °C (degree Celsius)
Q>0Q > 0: heat gained; Q<0Q < 0: heat lost.
Thermodynamics

Heat capacity of a body

C=cmC = cm
Symbols
  • CC — heat capacity of the body, J/K
  • cc — specific heat capacity, J/(kg·K)
  • mm — mass of the body, kg (kilogram)
Thermodynamics

Heat to vaporize a liquid at its boiling point

Q=LmQ = Lm
Symbols
  • QQ — heat of vaporization, J (joule)
  • LL — specific latent heat of vaporization, J/kg
  • mm — mass of the liquid, kg (kilogram)
Thermodynamics

Heat to melt a crystalline substance at its melting point

Q=λmQ = \lambda m
Symbols
  • QQ — heat of fusion, J (joule)
  • λ\lambda — specific latent heat of fusion, J/kg
  • mm — mass of the substance, kg (kilogram)
Thermodynamics

Heat released by complete combustion of a fuel mass

Q=qmQ = qm
Symbols
  • QQ — heat of combustion, J (joule)
  • qq — specific heat of combustion of the fuel, J/kg
  • mm — mass of the fuel, kg (kilogram)
Thermodynamics

Work done by a gas

W=pΔVW = p\Delta V
Symbols
  • WW — work done by the gas, J (joule)
  • pp — pressure of the gas, Pa (pascal)
  • ΔV\Delta V — change in volume of the gas, m³ (cubic meter)
Thermodynamics

First law of thermodynamics

Q=ΔU+WQ = \Delta U + W
Symbols
  • QQ — heat supplied to the gas, J (joule)
  • ΔU\Delta U — change in internal energy of the gas, J (joule)
  • WW — work done by the gas, J (joule)
QQ is heat supplied to the gas; WW is work done by the gas.
Thermodynamics

Heat balance equation

Q1+Q2+…=0Q_1 + Q_2 + \ldots = 0
Symbols
  • Q1,Q2,…Q_1, Q_2, \ldots — heats gained and lost by bodies (with signs), J (joule)
The algebraic sum of heats gained and lost in the process is zero.
Thermodynamics

Efficiency of a heat engine

η=WQ1⋅100%\eta = \frac{W}{Q_1} \cdot 100\%
Symbols
  • η\eta — efficiency of the heat engine, % (percent)
  • WW — useful work of the engine, J (joule)
  • Q1Q_1 — heat taken from the heater, J (joule)
Thermodynamics

Efficiency of an ideal heat engine (Carnot)

η=T1−T2T1⋅100%\eta = \frac{T_1 - T_2}{T_1} \cdot 100\%
Symbols
  • η\eta — efficiency of the ideal heat engine, % (percent)
  • T1T_1 — temperature of the hot reservoir (K), K (kelvin)
  • T2T_2 — temperature of the cold reservoir (K), K (kelvin)
T1T_1 and T2T_2 are reservoir temperatures in kelvins.