Water molecules are constantly moving back and forth between the vapor and liqui
ID: 511045 • Letter: W
Question
Water molecules are constantly moving back and forth between the vapor and liquid at equilibrium. (a) How much work per kg is required to evaporate liquid to vapor at equilibrium? Assume that the gas is only water vapor with a pressure of 611.2 Pa at a temperature of 273.15 K. (b) What is the change in the specic internal energy, the specic entropy, the specic Gibbs free energy, and the specic Helmholtz free energy due to the evaporation of liquid to vapor? The specic quantities should be per kg. Does it take more energy to break bonds in liquid or to do expansion work? What interpretation can you provide for the change in the specic Helmholtz free energy? (c) If the gas above the liquid included dry air with a total atmospheric pressure of 100,000 Pa, would the specic enthalpy dierence between the vapor and liquid change? Provide a calculation.
Explanation / Answer
(a) Work required (w)
= P (Vgas - Vliq)
= PVgas (As Vgas >> Vliq)
= P (RT/P)
= RT
= 8.314 J/mol.K * 273.15 K
= 2271 J/mol
= (2271*1000/18) J/Kg
= 126.16 kJ/Kg
(b) We know latent heat of evaporation of water = specific enthalpy of evaporation (dH)= 2260 kJ/Kg
specific internal energy (dE) = dH - w = 2260 - 126.16 = 2133.84 kJ/Kg
dS = dH/T = (2260 kJ/Kg) / (273.15 K) = 8.27 kJ/Kg. K
dG = dH - TdS = dH - T(dH/T) = 0
dA = dE - TdS = 2133.58 kJ/Kg - T(dH/T)
= 2133.58 kJ/Kg - dH
= -126.16 kJ/Kg
= -w
At phase transition internal energy change occur due to energy required in breaking of bonds. Expansion work denotes 'w'. Here dE > w, so energy required in breaking of bonds is greater than the energy required to do the expansion work.
As dA = -w, so all work done is required to change the Helmholtz free energy of the system. This is the maximum reversible work at constant temperature that is done by the gas.
(c) If pressure above the gas increases the boiling point of the water will also increase. From Kirchhoff equation:
d(H) /dT = Cp = Cp(steam) - Cp(water) < 0
Thus, the liquid has a bigger heat capacity than the steam. As boiling point increases with pressure heat capacity of water catches up with the enthalpy of steam and the difference decreases.
So with increasing pressure specific enthalpy difference between the vapor and liquid decreases.
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