Work (Isothermal Process)
Work for isothermal (constant T) expansion of ideal gas.
Variables
Derivation
W = ∫P dV = ∫(nRT/V) dV = nRT ln(V_f/V_i).
Your notes
Constants in this formula
Check value
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- 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
- Entropy Change (Ideal Gas) (Entropy) shares Moles, Gas constant, Final volume, Initial volume
- Internal Energy (Ideal Gas) (First Law) shares Moles, Gas constant, Temperature
- Root Mean Square Speed (Kinetic Theory) shares Temperature, Gas constant
- Most Probable Speed (Kinetic Theory) shares Temperature, Gas constant
- Mean Speed (Kinetic Theory) shares Temperature, Gas constant
- Heat Capacity Relation (First Law) shares Gas constant
Where this formula is listed
- Thermodynamics formulas, under First Law, alongside First Law of Thermodynamics, Adiabatic Process, Work (Adiabatic Process) and Enthalpy.
- In the thermodynamics list it comes after Work Done by Gas and before Internal Energy (Ideal Gas).
- 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 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).
