Practical Applications>

    Many commercial Pressure Cooker have pressure settings at Low (5.0 psi), Medium (10.0 psi),  and High (15.0 psi): the pressures are above the atmospheric pressure.   Boiling point of water is 100oC (212oF) under the normal atmospheric pressure (1 atm, or 14.7 psi).

 

What are the highest possible temperature of the cooker at the three pressure settings? Namely, find the boiling points of water at the three different  settings.

(1) At the Low Setting,
     Total Pressure =  (14.7+5.0)psi/(14.7 psi/atm) = 1.34 atm

     ln(P2/P1) = (DH/R)(1/T1-1/T2)
arranging this for T2 ,
       T2  =  [ 1/T1  - (R/DH)ln(P2/P1) ]-1
             =  [1/(100+273)K - (8.314 cal/(mol K))/40700cal*ln(1.34atm/1.00atm)]-1

             =  383 K   =  (381.5-273) oC = 110 oC = 231 oF

(2) At the Medium Setting,
     Total Pressure =  (14.7+10.0)psi/(14.7 psi/atm) = 1.68 atm
       T2  =  [ 1/T1  - (R/DH)ln(P2/P1) ]-1
             =  [1/(100+273)K - (8.314 cal/(mol K))/40700cal*ln(1.68atm/1.00atm)]-1

             =  388 K    =  (388.4-273) oC = 115 oC = 239 oF

(3) At the High Setting,
     Total Pressure =  (14.7+15.0)psi/(14.7 psi/atm) = 2.02 atm
       T2  =  [ 1/T1  - (R/DH)ln(P2/P1) ]-1
             =  [1/(100+273)K - (8.314 cal/(mol K))/40700cal*ln(2.02atm/1.00atm)]-1

             =  394 K    =  (394 - 273) oC = 121 oC = 250 oF