Suppose that you want to freeze 1 kg of water for a party, and only have 5 minut

Question

Suppose that you want to freeze 1 kg of water for a party, and only have 5 minutes to do it. Relying on nothing but your keen physical abilities, a dixicup, duct tape and a piece of string, you manage to build a refrigerator unit which can do the job.
The temperature inside the refrigeration unit is 273 K, and the temperature outside is 350 K. Since you are a brilliant UIUC student, assume that your refrigerator has the maximum possible efficiency. The Latent Heat of Fusion of water is 3.33×105 J/kg
Assume that the initial temperature of the water is 273 K.

1) What is the heat flow ( Q_ cold/time ) out of the Cold well per second in J/s? Hcold= Qcold/time= _____ J/s

3) What is the heat flow ( Q_hot/time ) into the Hot well per second in J/s? Hhot=Qhot/time= ______ J/s

4) How much POWER must you provide to drive your refrigerator in Watt W? (That is work done per second?) Power= ____ W

Explanation / Answer

Mass(m) = 1 kg
Time(t) = 5 minutes = 300 seconds
Tc = T_initial = 273 K
Th = 350 K
Lfus = 333 kJ/kg

a)What is the heat flow out of the Cold well per second in J/s?

QA = mLfus/t
QA = 1 ( 333 kJ / g ) / ( 300 s ) = 1.110 kJ/s ~1110kJ/s<-------
Maximum COP = ( Tc ) / ( Th - Tc ) = ( 273 K ) / ( 350 K - 273 K )
Maximum COP = 3.545 COP Units
WHP = QA / COP = 1110 J/s / 3.545 = 313 J/s = 313 W <---------------
QR = QA + WHP
QR = 1110 J/s + 313 J/s = 1423 J/s <------

b) What is the change (including the sign) in entropy in the water per second in J/(Ks)?
Qc = m*Lfus
Qc = 1*333
Qc = 333 kJ
Qc = Qc/t = 333/300

Qc = 1.11 kW

?S = -Qc_dot/Tc
?S = -1110/273
?S = -4.065934 W/K = -4.065934 J/Ks

c) What is the heat flow ( Q_hot/time ) into the Hot well per second in J/s?
? = Tc/Th-Tc = 273/350 - 273
? = 3.54545

? = Qc/Qh - Qc
3.54545 = 1.11 / Qh - 1.11
3.54545Qh - 3.9354495 = 1.11
Qh = 1.4231 kW = 1423.1 J/s

d) How much POWER must you provide to drive your refrigerator in Watt W?
W = Qh - Qc
W = 1423.1 - 1110
W = 313.1 W

Please verify the calculations, as they may be wrong but the logic used is correct.

I hope my answer helped.

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