What is the best possible coefficient of performance for a refrigerator that coo

Question

What is the best possible coefficient of performance for a refrigerator that cools an environment at-13.0 °C and exhausts heat to another environment at 47.0 °C? Number 4.33 How much work in joules must be done for a heat transfer of 3.725 x10s J from the cold environment? Number 860277.14 What is the cost of doing this, if the work costs 10.5 cents per 3.60 x10s J (a kilowatt-hour)? Number 25.09 cents How many joules of heat transfer occurs into the warm environment? Number 1232777.136J Incorrect

Explanation / Answer

a)

COP = Tc / (Th - Tc)

where,

Tc = 47 degree C = 320 K

Th = 260 K

COP = 260 / (320 - 260)

COP = 4.333

b)

W = Qc / COP

W = 1000 kcal / 4.333

W = 230.79 kcal

W = 860277.14 J

c)

cost = 230.79 kcal x (4186 J / 1 kcal) x ( 10.5 cent / 3.60 x 10^6)

cost = 2.82 cent

d)

W = Qh - Qc

Qh = W + Qc

Qh = 230.79 kcal + 1000 kcal

Qh = 1230.79 kcal

Qh = 1230.79 kcal x (4.186 kcal / 1 kcal)

Qh = 5152.1 kcal

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