# Verification of Boyle's Law

Everyone is familiar with Boyle's law $$PV = \text{constant}$$ if the temperature remains constant. You will measure and vary $$P$$ and $$V$$ for a trapped mass of air and see how good your system follow Boyle's law.

## Procedure

You need a syringe with one end closed and some air trapped in it, an identical extra syringe, support system for keeping the syringe fixed in vertical position, a pan suspended from the lower end of the syringe barrel, known weights.

Suppose, you put a weight $$W$$ in the pan. The piston will slide down and will stay at some position. Suppose, the pressure inside is $$P$$ and area of inner cross section is $$A$$. Let the weight of the piston plus the pan is $$W_0$$. Atmospheric Pressure = $$P_0$$. For equilibrium, $$PA+W+W_0=P_0A$$ or $$P=(P_0A-W-W_0)/A$$ or $$nRTA({1}/{V})=(P_0A-W_0)-W$$. Thus if you plot $$1/V$$ versus $$W$$, it should be a straight line.

So, look at the volume with zero weight. Then increase the weight in steps and every time measure the volume. Make a table and calculate $$1/V$$ for each value. Plot a graph $$1/V$$ versus $$W$$.

The piston and the barrel will have some friction. The piston can stay at different positions for the same weight. So you have to carefully determine the volume corresponding to a given weight. One way is to pull the piston a little and release, see where it stays while going up. Then push it a little and release, see where it stays while coming down. Take the average.

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