Carnot Refrigerator Efficiency and Energy Calculations | Homework Help

[lindsey4]

Homework Statement

An ideal refrigerator utilizes a carnot cycle operating between 0 and 25 degrees celsius. To turn 10 kg of water at 0 degrees celsius into 10 kg of ice at 0 degrees celsius,
a) how much heat is exhausted into the room?
b) how much energy must be supplied to the refrigerator?

Homework Equations

coefficient of performance of carnot refrigerator (Kcarnot): Tc/(Th-Tc)
n (funky n for efficiency thing)=Wout/Qh [but isn't that for engine]
K=Qc/W

The Attempt at a Solution

I'm guessing part A is Q so I'd have to find that somehow. And, for part B I think you use the last formula I put here and input Q to find W.

 

[haruspex]

coefficient of performance of carnot refrigerator (Kcarnot): Tc/(Th-Tc)
n (funky n for efficiency thing)=Wout/Qh [but isn't that for engine]

An ideal Carnot cycle is reversible, so W is the work, whether it's in or out.
The only thing that changes is how efficiency is defined. Equations not involving η are unchanged.
W = Q_H (1-T_C/T_H ) = Q_C (1-T_H/T_C )

I'm guessing part A is Q so I'd have to find that somehow.

There are two Qs: Q_H and Q_C. Which do you want for part A?

 

[Andrew Mason]

Homework Statement

An ideal refrigerator utilizes a carnot cycle operating between 0 and 25 degrees celsius. To turn 10 kg of water at 0 degrees celsius into 10 kg of ice at 0 degrees celsius,
a) how much heat is exhausted into the room?
b) how much energy must be supplied to the refrigerator?

Homework Equations

coefficient of performance of carnot refrigerator (Kcarnot): Tc/(Th-Tc)
n (funky n for efficiency thing)=Wout/Qh [but isn't that for engine]
K=Qc/W

The COP for the refrigerator is output/input where the output is the amount of heat removed from the cold reservoir, Qc and W is the work supplied: COP = Qc/W

Since W = Qh-Qc, and Th/Tc = Qh/Qc, you can express COP in terms of Th and Tc (your expression is correct).

For a) what do you need to find? (hint: it is one of W, Qh or Qc). For b) what do you need to find? (same hint)

AM