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# Example: Calculating work done on a gas

To illustrate how to use the equation for PV work, let’s imagine a bicycle pump. We will assume that the air in the bicycle pump can be approximated as an ideal gas in a piston. We can do work on the air in the pump by compressing it. Initially, the gas has a volume of 3.00L  We apply a constant external pressure of 1.10 atm to push down the handle of the bike pump until the gas is compressed to a volume of 2.50 L

How much work did we do on the gas?We can use the equation from the previous section to calculate how much work was done to compress the gas:

W = -Pexternal × ΔV

= -Pexternal ×(Vfinal × Vinitial)

If we plug in the values for Pexternal, Vfinal and Vinitial for our example, we get:

W = -1.10atm × (2.50L – 3.00L)

= -1.10atm × -0.05L

= 0.55L . atm

Let’s check the sign for the work to make sure it makes sense. We know the gas had work done on it, since the volume of the gas decreased. That means the value of work we calculated should be positive, which matches our result. Hooray! We can also convert our calculated work to Joules using the conversion factor:

w = 0.55 L.atm × 101.325 J / 1 L .atm = 56 J

Thus, we did 56 J f work to compress the gas in the bicycle pump from 3.00 L to 2.50 L