the boiling point of a liquid increases as the pressure above the liquid increas
ID: 981515 • Letter: T
Question
the boiling point of a liquid increases as the pressure above the liquid increases. In contrast to boiling food in an open pot, pressure cookers trap the steam, which raises the internal pressure, which raises the boiling point of water, causing a higher cooking temperature. A higher cooking temperature means that the food will cook faster. The instruction booklet for the pressure cooker indicates that its highest setting is 12.1 psi. You know that standard atmosheric pressure is 14.7 psi, so the booklet must mean 12.1 psi above Atoshperic pressure. At what temperature in degrees celsius will your food cook in this pressure cooker set on "high"? (The heat of vaporization of water is 4.07x10^4 J/mol)
Explanation / Answer
ln(P2/P1) = (Hvap/R)*((1/T1) - (1/T2))
P1 = 14.7 psi
T1 = 100 °C = (100 + 273.15 K) = 373.15 K
P2 = (14.7 psi + 12.1 psi) = 26.8 psi
T2 = unknown (what to solve for)
Hvap = 40.7 kJ mol^-1
R = 0.008314 JK^1mol^1
ln(26.8 psi/14.7 psi) = ((40.7 kJ mol^-1)/(0.008314 JK^1mol^1))*(1/373.15 K - 1/T)
Solving this, we get
T = 391.05 K
391.05 K = (391.05 - 273.15 °C) = 117.9 °C = 118 °C (to three sig figs)
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