Barometric pressure and boiling point

Our pressure cooker was a Prestige Skyline from the 1950s. The regulator is sticking up at the back.

A familiar object in the kitchen of my youth was our pressure cooker. It cooked the vegetables in a fraction of the time, saving significant amounts of energy and therefore cost.

Our pressure cooker was a stainless steel device equipped with a regulator that maintained an internal pressure of 2 atmospheres. I was thinking back to it the other day, and started wondering about the temperature of the superheated water inside the container. This can be calculated using the Clausius-Clapeyron equation

which approximates the slope of the liquid-vapor coexistence curve at vapor pressure P and boiling point temperature T. Using the mathematical identity

the Clausius-Clapeyron equation can also be written in the form

If we further assume that ΔH_vap is independent of temperature, integration of the above equation can be performed

If the vapor pressure P₁ is known at boiling point temperature T₁, this equation can be used to estimate the boiling point temperature T₂ at another pressure P₂.

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Worked Example

Water boils at 373.15K at a pressure of 1 atmosphere. At what temperature will water boil in a pressure cooker operating at a pressure of 2 atmospheres? The enthalpy of vaporization ΔH_vap of water at 373.15K is 40657 Jmol^-1 and the gas constant R is 8.3145 JK^-1mol^-1.

Strategy

Use the integrated Clausius-Clapeyron equation to solve for T₂

The SI units are:
T = K
R = JK^-1mol^-1
ΔH = Jmol^-1

The units of P₁ and P₂ are immaterial, so long as they are the same.

Note that P₁ and P₂ are vapor pressures. Since T₁ and T₂ refer to boiling point temperatures, the vapor pressures P₁ and P₂ will be the same as the externally applied pressures.

Calculation

Water in a pressure cooker operating at a pressure of two atmospheres boils at 394K, or 121°C. This explains why vegetables cook so fast in these devices.