Question

Why is q positive in an isothermal expansion?

Answer 1

Because it has to flow into the system for it to expand without changing the temperature.

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An isothermal expansion is what it sounds like... increasing volume at constant temperature.

For an ideal gas, the internal energy is only a function of temperature, so the first law of thermodynamics reads

`cancel(DeltaU)^(0) = q + w`

where `DeltaU` is the change in internal energy, `q` is heat flow, and `w` is work from the perspective of the SYSTEM.

Thus, `q = -w`. Since work is from the perspective of the SYSTEM, expansion work requires energy, and so, `w < 0`. As a result,

`-q < 0`

and that therefore means `q > 0`.

If it were a nonideal gas, it could expand not as easily (i.e. attractive intermolecular forces dominate), or it could expand too easily (i.e. repulsive intermolecular forces dominate). As a result, `DeltaU ne 0` for such a nonideal gas.