Pressure of the Void To high precision, standard atmospheric pressure equals 101.32 kPa and will support a barometric column of mercury 760 millimeters in height. This is by definitio; it is an assumed surface-of-Earth average. Torricelli assumed the pressure in the void above the mercury column to be zero. The actual non-zero pressure is called the vapor pressure of mercury at 25°C. Use the information of the sketch to Calculate the "Pressure of the Void."

♦  Application of the hydrostatic equation requires a known pressure. The atmospheric pressure, at the air/mercury interface, is 101.32 kPa. Since the interface is flat, the pressure of the air and the pressure of the mercury are the same.

patm = 101,320 Pa    and     p1,Hg = 101,320 Pa

The pressure of the mercury gas (trapped above ans seen as a "void") at a height of 760 mm above the air/mercury interface is less than 101,320 Pa by the pressure difference:  ρHg go(760mm).

The density of liquid mercury is 13,594.58 kg/cubic meter (great precision must be carried because this calculation entails both very large and very small numbers).

patm - ρHg go(760mm) = pHg,vapor

101,320 N/m2 - (13,594.58 kg/m3)(9.804m/s2)(0.760m) = pHg,vapor

27 Pascals = pHg,vapor

This example is subject to error because the numbers are very large and very small.