| Boyle's Law |
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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 |
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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,  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,  |
. The unknown pressure Pi can be reduced to a function of the height difference h,