Entropy Change (Ideal Gas)

\Delta S = nC_V \ln\frac{T_f}{T_i} + nR\ln\frac{V_f}{V_i}

Entropy change for ideal gas between two states.

Variables

ΔS

Entropy change

Change in entropy

In SI units: kg·m²/(s²·K)

J/K

Moles

Amount of gas

mol

C_V

Molar heat capacity

At constant volume

In SI units: kg·m²/(s²·mol·K)

J/(mol·K)

T_f

Final temperature

Final temp

T_i

Initial temperature

Initial temp

Gas constant

8.314

In SI units: kg·m²/(s²·mol·K)

J/(mol·K)

V_f

Final volume

m³

V_i

Initial volume

m³

Derivation

dS = dQ/T = (nC_V dT + PdV)/T, integrate.

Your notes

0/5000

Constants in this formula

Molar Gas Constant

8.314 462 618…. Exact by definition.

J/(mol·K)

Other thermodynamics formulas with the same quantities

Work (Isothermal Process) (First Law) shares Moles, Gas constant, Final volume, Initial volume
Internal Energy (Ideal Gas) (First Law) shares Moles, Gas constant
Root Mean Square Speed (Kinetic Theory) shares Gas constant
Heat Capacity Relation (First Law) shares Gas constant
Clausius Inequality (Second Law) shares Entropy change
Most Probable Speed (Kinetic Theory) shares Gas constant

Where this formula is listed

Thermodynamics formulas, under Entropy, alongside Boltzmann Entropy, Gibbs Free Energy and Helmholtz Free Energy.
In the thermodynamics list it comes after Mean Speed and before Boltzmann Entropy.
Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Entropy Change (Ideal Gas) formula?

Entropy Change (Ideal Gas) is written ΔS = nC_V ln(T_f/T_i) + nR ln(V_f/V_i). Entropy change for ideal gas between two states. It belongs to Thermodynamics, under Entropy.

What are the units in ΔS = nC_V ln(T_f/T_i) + nR ln(V_f/V_i)?

In SI units, ΔS is entropy change, measured in kg·m²/(s²·K); n is moles, measured in mol; C_V is molar heat capacity, measured in kg·m²/(s²·mol·K); T_f is final temperature, measured in K; T_i is initial temperature, measured in K; R is gas constant, measured in kg·m²/(s²·mol·K); V_f is final volume, measured in m³; V_i is initial volume, measured in m³.

How is the Entropy Change (Ideal Gas) formula derived?

dS = dQ/T = (nC_V dT + PdV)/T, integrate. The result is ΔS = nC_V ln(T_f/T_i) + nR ln(V_f/V_i).