Thermodynamics
Work (Isothermal Process)
Work for isothermal (constant T) expansion of ideal gas.
Variables
WJ
Work
Work by gas
nmol
Moles
Amount of gas
RJ/(mol·K)
Gas constant
8.314
TK
Temperature
Constant temperature
V_fm³
Final volume
Final volume
V_im³
Initial volume
Initial volume
Derivation
W = ∫P dV = ∫(nRT/V) dV = nRT ln(V_f/V_i).
Your notes
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Common questions
What is the Work (Isothermal Process) formula?
Work (Isothermal Process) is written W = nRTlnV_f/Vᵢ. Work for isothermal (constant T) expansion of ideal gas. It belongs to Thermodynamics, under First Law.
What are the units in W = nRTlnV_f/Vᵢ?
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 = nRTlnV_f/Vᵢ.