Trabalho Isotérmico
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
W_iso = nRT ln(V₂/V₁)
About this calculator
This calculator determines the work done by an ideal gas during an isothermal expansion or compression, i.e., at constant temperature. The formula W = nRT ln(V₂/V₁) describes reversible work. The user inputs the number of moles (n), temperature (T), and initial (V₁) and final (V₂) volumes.
Isothermal work is calculated using the ideal gas law. Temperature must be provided in kelvin. If V₂ > V₁, work is positive (expansion, gas does work on surroundings). If V₂ < V₁, work is negative (compression, work is done on the gas).
This tool is useful for thermodynamics students, engineers, and professionals analyzing isothermal processes, such as in heat engines, compressors, or expanders. It helps understand the relationship between volume and work under constant temperature conditions.
Caution: the formula assumes a reversible process and ideal gas. Real processes may involve irreversibilities. Ensure temperature is in kelvin and volumes in the same unit. The natural logarithm requires V₂ and V₁ positive.
Frequently asked questions
What does isothermal work mean?
It is the work done by an ideal gas during a transformation at constant temperature, calculated by W = nRT ln(V₂/V₁).
Do I need to use temperature in kelvin?
Yes, temperature must be in kelvin for the gas constant R (8.314 J/mol·K) to be compatible.
What if the final volume is less than the initial?
In that case, work is negative, indicating that the surroundings do work on the gas (compression).
Does the calculator work for real gases?
The formula is for ideal gases. For real gases, the result is an approximation, especially at high pressures.
Can I use liters or cubic meters?
Yes, as long as both volumes are in the same unit. The result will be in joules if using R = 8.314 J/mol·K and volumes in m³.