Question

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

Answer 1

1751399.8902 J

Step-by-step explanation:

m = Mass of water = 74.6 kg

`\Delta H_f` = Latent heat of fusion =
`3.34* 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

`(Q_c)/(Q_h)=(T_c)/(T_h)\\\Rightarrow Q_h=(Q_cT_h)/(T_c)\\\Rightarrow Q_h=(m\Delta H_fT_h)/(T_c)\\\Rightarrow Q_h=(74.6* 3.34* 10^5* (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* 3.34* 10^5\\\Rightarrow E=1751399.8902\ J`

The energy supplied to the device is 1751399.8902 J