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ID: 591579 • Letter: A
Question
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2. Find the change in Gibbs energy if 1.0 mol of liquid water is pressurized at 0.0 eC from 1.0 atm to 10.0 atm. State any assumptions. (20%) 3. Consider an ideal refrigerator operating between 0°C and 25°C. The refrigerator is to produce 1.0 g of ice each second from water at 0°C. How much work must be done per second? The molar heat of fusion of water is 6.0095 kJ/mol. (20%)
Explanation / Answer
2. dG = -SdT+VdP
The Gibbs free energy of the system at constant temperature is
dG = Vdp
dG = nRT/p dp (According to the ideal gas equation).
G = nRT ln(p2/p1) [APPROXIMATION = Assuming the volume does not change in the pressure range of p1 to p2.]
= 1 . 8.314 J/K.273K ln(10/1)
= 5226.228 J/moles.
3. THe efficiency (e) of the refigrator is given by the equation
e = Q/W = T2/(T1-T2) Where T1 is the temperature of the hot junction such that T2>T1) Q is the heat taken, W is the work done
Q = Heat released for the 1gm of ice per second is 1/18 * 6.0095 KJ = 0.33386 KJ = 333.86 Joules.(Heat of fusion of ice is given and we need to calculate the heat released for the ice)
THus putting the values in the equation for efficiency
e = 333.86/W = 273/(298-273) = 10.92
W = 1/10.92 * 333.86 Joules = 30.57 Joules per second.
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