Question

At what temperature will water boil at Lake Tahoe? Lake Tahoe is approximately 1900 m above the sea level. The molar mass of air is 29.0 g/mol. Assume that air pressure at sea level is 1.00 atm and the air temperature is constant with elevation at 20 degrees Celsius. The molar heat of vaporization of water is 41.0 kJ/mol.

Answer 1

Pressure varies with altitude as

P= Po*e(-Mgh/RT), M= Molar mass of air = 29 g/mole= 29*10-3 kg/mole, R= 8.314 J/mole, T= temperature in K=20+273= 293K, Po= 1 atm

At h= 1900m

P= 1*exp{(-29*10-3*9.8*1900/(8.314*293)}=0.8 atm

Boiling temperature is defined as the temmperature at which the vapor pressure = 0.8 atm

From Classisus-Clayperon equation

ln(P2/P1)= (deltaH/R)*(1/T1-1/T2), P2= 1 atm, T2= 100+273=373K, P1=0.8, T1=?, deltaH= latent heat of vaporization= 41*1000J/mole

ln(1/0.8)= (41*1000/8.314)*(1/T1-1/373)

4.52*10^-5= 1/T1-1/373

1/T1= 0.00272, T1= 366.8K= 366.8-273= 93.8 deg.c

Water boils at 93.8 deg.c at 1900m height.