A heat exchanger is used to warm apple cider using steam as the heat source. The cider is heated from an initial temperature of 4 degrees celcius to a final temperature of 65 degree celcius. The steam enters the heat exchanger as 50% quality steam and exits as water condensate at 85 degrees celcius. Calculate the mass of steam required to heat 150 Kilograms of cider. (For the cider, assume the Cp = 3.651 KJ/Kg degrees celcius and latent heat = 280.18 KJ/Kg)
To calculate the mass of steam required to heat the cider, we need to determine the amount of heat transfer required.
The heat transfer equation is given by:
Q = m * Cp * ΔT + m * H
Where:
Q = Heat transfer (in kilojoules)
m = Mass of the substance (in this case, the cider) (in kilograms)
Cp = Specific heat capacity of the substance (in kilojoules per kilogram per degree Celsius)
ΔT = Temperature change (final temperature - initial temperature) (in degrees Celsius)
H = Latent heat of the substance (in kilojoules per kilogram)
Given:
Initial temperature of cider (T1) = 4°C
Final temperature of cider (T2) = 65°C
Specific heat capacity of cider (Cp) = 3.651 KJ/Kg°C
Latent heat of steam (H) = 280.18 KJ/Kg
Using the above values, let's calculate the heat transfer required to heat the cider:
ΔT = T2 - T1 = 65°C - 4°C = 61°C
Q = (m * Cp * ΔT) + (m * H)
Q = (150 Kg * 3.651 KJ/Kg°C * 61°C) + (150 Kg * 280.18 KJ/Kg)
Now, we can rearrange the equation to solve for the mass of steam (m):
m = Q / (Cp * ΔT + H)
Substituting the values into the equation:
m = ((150 Kg * 3.651 KJ/Kg°C * 61°C) + (150 Kg * 280.18 KJ/Kg)) / (3.651 KJ/Kg°C * 61°C + 280.18 KJ/Kg)
Now, let's calculate the mass of steam required.