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°C to a final temperature of 65°C. The steam enters the heat exchanger as 50% quality steam and exits as water condensate at 85°C. Calculate the mass of steam required to heat 150 kg of cider. (For the cider, assume the Cp=3.651 kJ/kg°C, and latent heat=280.18 kJ/kg.)

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To calculate the mass of steam required to heat the cider, we need to determine the amount of heat energy needed to raise the temperature of the cider and the amount of heat energy provided by the steam.

1. Calculate the heat energy required to raise the temperature of the cider:
The formula to calculate the heat energy required is given by:
Q = m * Cp * ΔT
where Q is the heat energy, m is the mass of the cider, Cp is the specific heat capacity of the cider, and ΔT is the change in temperature.

Given:
m (mass of cider) = 150 kg
Cp (specific heat capacity of cider) = 3.651 kJ/kg°C
ΔT (change in temperature) = 65°C - 4°C = 61°C

Substituting the given values into the formula, we get:
Q = 150 kg * 3.651 kJ/kg°C * 61°C
Q = 33724.35 kJ

2. Determine the heat energy provided by the steam:
The steam enters as 50% quality steam and exits as water condensate at 85°C. We can calculate the heat energy transferred from steam to the cider using the formula:
Q = m * (hfg + Cp * ΔT2)
where Q is the heat energy, m is the mass of steam, hfg is the latent heat of vaporization/condensation, Cp is the specific heat capacity of water, and ΔT2 is the change in temperature.

Given:
ΔT2 = 85°C - 100°C = -15°C (as steam condenses to water at 100°C)
hfg (latent heat of vaporization/condensation) = 280.18 kJ/kg
Cp (specific heat capacity of water) = 4.186 kJ/kg°C (assuming water as the final state)

Substituting the given values into the formula, we get:
Q = m * (280.18 kJ/kg + 4.186 kJ/kg°C * -15°C)
Q = m * (280.18 kJ/kg - 62.79 kJ/kg)
Q = m * 217.39 kJ/kg

3. Equate the heat energy provided by the steam to the heat energy required by the cider:
Since the heat energy provided by the steam is equal to the heat energy required by the cider, we can write:
33724.35 kJ = m * 217.39 kJ/kg

4. Calculate the mass of steam required:
Rearrange the equation to solve for the mass of steam (m):
m = 33724.35 kJ / 217.39 kJ/kg
m = 155.15 kg

Therefore, the mass of steam required to heat 150 kg of cider is approximately 155.15 kg.