# Thermodynamic Work

A common type of work associated by a chemical process is through gas expansion or compression. An example that you have experienced is the energy produced from the combustion of gasoline. Gasoline combustion is used to create expanding gases in the cylinders of your car's engine that push out the pistons. This motion is then translated into the motion of the car. Let's look at the work associated with moving a piston.

Now remember that work is defined as a Force applied over a distance is

|Work| = |F · Δh|,

where Δh = h_{final} - h_{initial}. We write the absolute value of work since we still need to make sure the sign of work agrees with our earlier definitions. Using the definition of p = F/A, and recognizing A · Δh as the change in volume of the cylinder, we can write the work associated with moving a piston a distance Δh as

|Work| =p · A · Δh = p · ΔV

where ΔV = V_{final} - V_{initial}. If ΔV is positive then the gas is expanding and doing work on the surroundings. So work should be negative

Work = - p · ΔV

This equation is true in general, not just for pistons.

**Calculate the work associated with the expansion of a gas from 46 L to 64 L at a constant external pressure of 15 atm.**

First we calculate

ΔV = 64 L - 46 L = 18 L

Using P=15 atm, we can then calculate

Work = - p · ΔV = (15 atm) (18 L) = -270 atm-L

Using the conversion between atm-L and Joules of

1 L-atm = 101.325 J

Thus, we obtain

So, when the gas expands it does 27.4 kJ of work on its surroundings (*i.e.*, 27.4 kJ of energy flows out of the system so the work is negative).

Note: These quizzes use E, instead of U for the internal energy

#### Homework from Chemisty, The Central Science, 10th Ed.

5.27, 5.47, 5.49, 5.51