# How would you calculate DeltaE of a gas for a process in which the gas absorbs 35 J of heat and does 8 J of work by expanding?

Jul 10, 2016

This is asking you to apply the first law of thermodynamics:

$\stackrel{\text{otherwise known as}}{\stackrel{\Delta U}{\overbrace{\setminus m a t h b f \left(\Delta E\right)}}} \setminus m a t h b f \left(= q + w\right)$

where:

• $\Delta E$ is the change in internal energy.
• $q$ is the heat flow in the thermodynamic process.
• $w$ is the expansion/compression work performed by the gas or on the gas.

Since the work is done by the gas (rather than on the gas) through the expansion, $w < 0$. Work is also defined as:

$w = - P \Delta V = - P \left({V}_{2} - {V}_{1}\right)$

where final volume ${V}_{2}$ is larger than initial volume ${V}_{1}$ in an expansion, i.e. when work is negatively-signed. If work were to be positively-signed, then ${V}_{2}$ would be smaller than ${V}_{1}$.

Since the gas absorbs heat, heat flows into the gas, i.e. $q > 0$.

Therefore:

$\textcolor{b l u e}{\Delta E} = \left(\text{35 J") + (-"8 J}\right)$

$=$ color(blue)("27 J"