Milk is flowing through a heat exchanger at a rate of 2000kg/h. he heat exchanger supplies 111,600kJ/h. The outlet temperature of the product is 95C. Determine the inlet temperature of the milk.
The product specific heat is 3.9kJ/(kg*C)
m_dot = 2000 kg/h
q = 111600 kJ/h
T_final = 95C
C_p = 3.9 kJ/(kgC)
equation: q = m_dot*c_p*(T_initial-T_final)
plug in all the value and solve for T_initial
*NOTE* remeber deta_T both in C and K is the same. So don't worry
m_dot = 2000 kg/h
q = 111600 kJ/h
T_final = 95C
C_p = 3.9 kJ/(kgC)
48
80.69
Oh, the heat exchanger is really milking it, isn't it? Well, to determine the inlet temperature of the milk, we can use the equation:
Heat gained = Mass flow rate x Specific heat x (Outlet temperature - Inlet temperature)
In this case, the heat gained is given as 111,600 kJ/h, the mass flow rate is 2000 kg/h, and the specific heat is 3.9 kJ/(kg*C). We know the outlet temperature is 95C, and we need to find the inlet temperature.
So, plugging in the values:
111600 = 2000 x 3.9 x (95 - Inlet temperature)
Now, let's solve for the inlet temperature:
111600 = 7800 x (95 - Inlet temperature)
Divide both sides by 7800:
14.3077 = 95 - Inlet temperature
Rearrange the equation:
Inlet temperature = 95 - 14.3077
And voila!
Inlet temperature = 80.6923 C
Looks like our milky milk should be coming in at a temperature of approximately 80.6923 degrees Celsius.
To determine the inlet temperature of the milk, we can use the heat balance equation which states that the heat gained or lost by a substance is equal to the mass flow rate multiplied by the specific heat capacity multiplied by the change in temperature.
In this case, we know the following:
- Mass flow rate of the milk (m): 2000 kg/h
- Heat supplied by the heat exchanger (Q): 111,600 kJ/h
- Outlet temperature of the milk (T_out): 95°C
- Specific heat capacity of the milk (C): 3.9 kJ/(kg°C)
We can rearrange the equation to solve for the inlet temperature (T_in):
Q = m * C * (T_out - T_in)
Substituting the known values:
111,600 = 2000 * 3.9 * (95 - T_in)
Simplifying the equation:
111,600 = 7800 * (95 - T_in)
Dividing both sides of the equation by 7800:
14.3077 = 95 - T_in
Rearranging the equation:
T_in = 95 - 14.3077
T_in = 80.6923°C
Therefore, the inlet temperature of the milk is approximately 80.6923°C.