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Problem 3.
How many btu are needed to change 10 pounds of ice at 5 degree Fahrenheit to steam at 250 degree Fahrenheit?
Solution:
The first step: we convert the temperatures given in Fahrenheit into the temperatures in Celsius:
5 degree Fahrenheit = -15 C
250 degree Fahrenheit = 121 C
Then we can see that initially we have m=10 pounds = 4.5 kg of ice and finally we have m = 4.5 kg of vapor. Therefore the whole process can be considered as the combination of the following processes:
(1) heating the ice from -15 C to 0 C;
(2) melting of ice at fixed temperature 0 C. After this process the ice becomes water.
(3) heating the water from 0 C to 100 C.
(4) vaporization of water at fixed temperature100 C. After this process the water becomes vapor.
(5) heating the vapor from 100 C to 121 C.
Process (1): the heat required to change the temperature of the ice is determined by the specific heat of ice:
The specific heat of ice is 2060 J/kg C. Then
Process (2): the heat required to melt the ice is determined by the specific latent heat of fusion:
The specific latent heat of fusion is 334000 J/kg. Then
Process (3): the heat required to change the temperature of the water is determined by the specific heat of water:
The specific heat of water is 4186 J/kg C. Then
Process (4): the heat required to vaporize the water is determined by the specific latent heat of vaporization:
The specific latent heat of vaporization is 2260000 J/kg. Then
Process (5): the heat required to change the temperature of the vapor is determined by the specific heat of vapor:
The specific heat of vapor is 1870 J/kg C. Then
Then the total heat is
We can convert the joule in btu:
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