Energy Balance Problem: Milk is flowing through a heat exchanger at a rate of 2000 kg/h. The heat exchanger supplies 111,600 kJ/h of steam as energy (Q). The outlet temperature of the heated milk is 95°C. The milk specific heat (Cp) is 3.9 kJ/(kg °C). Assume that the reference temperature is 0 degree Celsius.
I may be dense but I don't see a question here.
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To solve this energy balance problem, we will use the following equation:
Q = m * Cp * (T2 - T1)
Where:
Q = Energy supplied by the steam (in kJ/h)
m = Mass flow rate of the milk (in kg/h)
Cp = Specific heat capacity of milk (in kJ/(kg °C))
T2 = Outlet temperature of the heated milk (in °C)
T1 = Reference temperature (in °C)
Given:
m = 2000 kg/h
Q = 111,600 kJ/h
T2 = 95°C
Cp = 3.9 kJ/(kg °C)
T1 = 0°C (since this is the reference temperature)
Plugging in the values into the equation, we have:
111,600 = 2000 * 3.9 * (95 - 0)
Simplifying:
111,600 = 2000 * 3.9 * 95
111,600 = 741,000
Therefore, the equation is not balanced. Please check your calculations and the given parameters once again.
To solve this energy balance problem, we need to calculate the amount of energy transferred to the milk in the heat exchanger. Here are the steps to determine the energy transfer:
Step 1: Calculate the heat transferred to the milk using the formula:
Q = m*Cp*(Tout - Tin)
Where:
Q = Heat transferred to the milk (in kJ/h)
m = Mass flow rate of milk (in kg/h)
Cp = Specific heat of milk (in kJ/(kg °C))
Tout = Outlet temperature of the milk (in °C)
Tin = Inlet temperature of the milk (in °C)
Given values:
m = 2000 kg/h
Cp = 3.9 kJ/(kg °C)
Tout = 95 °C
Tin = 0 °C (reference temperature)
Step 2: Substitute the given values into the formula to calculate Q.
Q = 2000 kg/h * 3.9 kJ/(kg °C) * (95 °C - 0 °C)
Q = 2000 * 3.9 * 95 kJ/h
Q = 741,000 kJ/h
Step 3: Compare the calculated heat transferred to the heat supplied by the steam.
Given values:
Heat supplied by steam (Q) = 111,600 kJ/h
The heat supplied by the steam is greater than the calculated heat transferred to the milk. Therefore, the heat exchanger is capable of supplying the required amount of energy to heat the milk to the outlet temperature.