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Boyle's Law

Boyle's Law, proposed by Robert Boyle in 1662, states that for a closed isothermal (constant temperature) system, the product of the pressure (P) and volume (V) is a constant,

Equivalently, the product at two different states must be the same,

McLeod Gages
Suppose that initial pressure and volume in a McLeod Gage are given by,

P1 = Pi

V1 = V + A·h0

where V is the reservoir volume and A is the cross-sectional area of the sealed tube, as shown schematically below.

Suppose that the final compressed pressure and volume are given by,

P2 = Pgage

V2 = A·h

According to Boyle's law, we have,

For a typical manometer, . The unknown pressure Pi can be reduced to a function of the height difference h,

Furthermore, the volume of the reservoir is usually much larger than the tube,

V » A·(h0-h)

This allows us to drop the area term, resulting in a simple quadratic function for the pressure,