Thermodynamics

Work (Isothermal Process)

W=nRTln⁡VfViW = nRT\ln\frac{V_f}{V_i}

Work for isothermal (constant T) expansion of ideal gas.

Variables

W
Work
Work by gas
In SI units: kg·m²/s²
J
n
Moles
Amount of gas
Allowed values: greater than 0
mol
R
Gas constant
8.314
In SI units: kg·m²/(s²·mol·K)
Allowed values: greater than 0
J/(mol·K)
T
Temperature
Constant temperature
Allowed values: greater than 0
K
Vf
Final volume
Final volume
Allowed values: greater than 0
m³
Vi
Initial volume
Initial volume
Allowed values: greater than 0
m³

Derivation

W = ∫P dV = ∫(nRT/V) dV = nRT ln(V_f/V_i).

Your notes

0/5000

Constants in this formula

R
8.314 462 618…. Exact by definition.
J/(mol·K)

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

  • n = 2 mol (Moles)
  • R = 8.314 462 618… J/(mol·K) (Gas constant)
  • T = 3 K (Temperature)
  • Vf = 4 m³ (Final volume)
  • Vi = 5 m³ (Initial volume)

Result: W = -11.131912 J

Other thermodynamics formulas with the same quantities

Where this formula is listed

Common questions

What is the Work (Isothermal Process) formula?

Work (Isothermal Process) is written W = nRT ln(V_f/V_i). Work for isothermal (constant T) expansion of ideal gas. It belongs to Thermodynamics, under First Law.

What are the units in W = nRT ln(V_f/V_i)?

In SI units, W is work, measured in kg·m²/s²; n is moles, measured in mol; R is gas constant, measured in kg·m²/(s²·mol·K); T is temperature, measured in K; V_f is final volume, measured in m³; V_i is initial volume, measured in m³.

How is the Work (Isothermal Process) formula derived?

W = ∫P dV = ∫(nRT/V) dV = nRT ln(V_f/V_i). The result is W = nRT ln(V_f/V_i).