Question

A maximum efficiency refrigerator is switched on for the first time. It has a 150 L capacity and is to operate in a room that is 25 degrees Celsius and maintain an inner temperature of 5 degrees Celsius.

A) What is the maximum amount of electrical work needed to cool it too it's operating temperature?

B) How much work is needed if six pack of 350 mL beers is placed in the fridge before cooling ? ( Assume cans, beers start at 25 degrees Celsius and can be modeled as water)

Answer 1

Assuming the density of solution in the bottle is 1 gm/ cc= 1000g/L, specific heat of water= 4.184 J/gm.deg.c

mass of 150 L= 1000g/L*150 L= 150*1000 gm= 1.5*10⁵ gm

heat to be removed = mass of bottle* specific heat of solution in the bottle* temperature difference=1.5*10⁵*4.184*20 J=1.3*10⁷ Joules

The Cop is maximum when the cycle is Carnot. For Carnot cycle

COP= QC/W, W= amount of work, Qc= heat to be removed

COP = TC/(TH-TC)= (25+273)/20 = 14.9

W= QC/COP = 1.3*10⁷ /14.9 joules =853878 joules

for 6 pack 350 ml beers, mass= 350*1000*6 gm=2.1*10⁶ gm

heat to be removed= 2.1*10⁶*4.184*20= 1.8*10⁸ Joules

W=QC/COP= 1.8*10⁸/14.7 =1.2*10⁷ joules