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sergejj [24]
3 years ago
15

An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0 degrees Celsius a

nd rejects heat to a room at a temperature of 19.2 degrees Celsius. Suppose that liquid water with a mass of 74.6kg at 0.0 degrees Celsius is converted to ice at the same temperature. Take the heat of fusion for water to be L_f = 3.34*10^5 J/kg.
How much energy E must be supplied to the device?

Express your answer in joules
Physics
1 answer:
avanturin [10]3 years ago
6 0

Answer:

1751399.8902 J

Explanation:

m = Mass of water = 74.6 kg

\Delta H_f = Latent heat of fusion = 3.34\times 10^5\ J/kg

T_h = 19.2°C

T_c = 0°C

We have the equation for cold body

Q_c=m\Delta H_f

We have the equation

\dfrac{Q_c}{Q_h}=\dfrac{T_c}{T_h}\\\Rightarrow Q_h=\dfrac{Q_cT_h}{T_c}\\\Rightarrow Q_h=\dfrac{m\Delta H_fT_h}{T_c}\\\Rightarrow Q_h=\dfrac{74.6\times 3.34\times 10^5\times (19.2+273.15)}{0+273.15}\\\Rightarrow Q_h=26667799.8902\ J

Energy rejected to the room is 26667799.8902 J

Energy supplied to the device is given by

E=Q_h-m\Delta H_f\\\Rightarrow E=26667799.8902-74.6\times 3.34\times 10^5\\\Rightarrow E=1751399.8902\ J

The energy supplied to the device is 1751399.8902 J

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