# How do you find q for isothermal processes?

Jul 24, 2016

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

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

${\cancel{\Delta U}}^{0} = q + w$

And we just get:

$\textcolor{b l u e}{- q = w = - P \Delta V}$

where:

• $q$ is the heat flow in $\text{J}$.
• $w$ is the expansion/compression work in $\text{J}$.
• $\Delta V$ is the change in volume in $\text{L}$. 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 $\text{bar}$ or $\text{atm}$.

If $\text{atm}$, you use "8.314472 J"/("0.082057 L"cdot"atm") for the conversion unit.