MasteringPhysics Thermodynamics problem?

Question

I have slight issues with the following problem:
"The Kwik-Freez Appliance Co wants you to design a food freezer that will keep the freezing compartment at -5.00 C and will operate in a room at 20.0 C. The freezer is to make 5.40 kg  of ice at 0 C , starting with water at 20.0 C."

The values are in degrees Centigrade. Could someone please explain how to solve it? The questions are:

Part A: Find the least possible amount of electrical energy needed to make this ice.

Part B: Find the smallest possible amount of heat expelled into the room.

Thanks in advance.

Anonymous · Accepted Answer

Part A: 

W = m (c_water) δT + m (L_ice)

W = 5400 (1) (20 - 0) + 5400 (80) 

W = 5.4 E5 cal

W = (5.4 E5)(4.18) = 2.257 E6 Joules


Part B: 

efficiency of freezer is

η = 1 - T2/T1 = W/Q

η = 1 - (-5 + 273)/(20 + 273)

η = 8.53 %

Q = W/η = 2.257 E6 / 8.53 % = 2.645 E7 Joules

the smallest possible amount of heat expelled into the room is :

(100 - 8.53)% (2.645 E7) = 2.419 E7 Joules
==================================

note:
c_water = 1 cal/gr °C
c_ice = 0.5 cal/gr °C
L_ice = 80 cal/gr

MasteringPhysics Thermodynamics problem?

1 Answer