Question

How do you find q for isothermal processes?

Answer 1

In isothermal processes, we know that by definition, the temperature is constant.

The internal energy `DeltaU` only depends on temperature for ideal gases, so `DeltaU = 0` in an isothermal process. Therefore, the first law of thermodynamics becomes:

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

And we just get:

`color(blue)(-q = w = -PDeltaV)`

where:

• `q` is the heat flow in `"J"`.
• `w` is the expansion/compression work in `"J"`.
• `DeltaV` is the change in volume in `"L"`. Note that `"8.314472 J"/("0.083145 L"cdot"bar")` is a convenient conversion unit.
• `P` is a single pressure. It tends to be in `"bar"` or `"atm"`.

If `"atm"`, you use `"8.314472 J"/("0.082057 L"cdot"atm")` for the conversion unit.