Question

An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0 ∘C and rejects heat to a room at a temperature of 22.5 ∘C. Suppose that liquid water with a mass of 85.7 kg at 0.0 ∘C is converted to ice at the same temperature. Take the heat of fusion for water to be Lf = 3.34×105 J/kg .How much energy E must be supplied to the device?

Answer 1

Answer:

2.36 x 10^6 J

Explanation:

Tc = 0°C = 273 K

TH = 22.5°C = 295.5 K

Qc = heat used to melt the ice

mass of ice, m = 85.7 Kg

Latent heat of fusion, L = 3.34 x 10^5 J/kg

Let Energy supplied is E which is equal to the work done

Qc = m x L = 85.7 x 3.34 x 10^5 =  286.24 x 10^5 J

Use the Carnot's equation

$\frac{Q_{H}}{Q_{c}}=\frac{T_{H}}{T_{c}}$

$Q_{H}=286.24\times 10^{5}\times \frac{295.5}{273}$

QH = 309.8 x 10^5 J

W = QH - Qc

W = (309.8 - 286.24) x 10^5

W = 23.56 x 10^5 J

W = 2.36 x 10^6 J

Thus, the energy supplied is 2.36 x 10^6 J.