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Isothermal process
Intermediate
Constant temperature; ΔU=0.
W = nRT ln(V₂/V₁)At constant temperature, ΔU = 0 for an ideal gas, so Q = W = nRT ln(V₂/V₁). On a PV diagram it's a hyperbola.
1 mol at 300 K doubling in volume does 1.73 kJ.
Needs slow contact with a heat reservoir.
In more detail
An isothermal process occurs at constant temperature. For an ideal gas, the internal energy stays constant, so all heat added becomes work done.
Real-world uses
- Slow compression of gases in cylinders approximates an isothermal process.
- Physics textbooks use isothermal processes to illustrate work.
- A gas slowly compressed in a tank while in contact with a large water bath stays at constant temperature.
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Frequently asked questions
Why is the internal energy constant?
Because the temperature is constant, and for an ideal gas internal energy depends only on temperature.
Is it fast or slow?
It requires slow processes that allow heat exchange with surroundings.
Why is internal energy unchanged in an isothermal process?
For an ideal gas, internal energy depends only on temperature, so constant temperature means no change in internal energy.
Related topics in Heat & Thermodynamics
Avogadro's number · Internal energy · First law of thermodynamics · Adiabatic process · Isobaric process · Isochoric process