Answer :
The specific heat of the sugar syrup in kJ kg-1 °C is 0.94955 kJ kg-1 °C. The rate of heating, in kJ S-1, is 2874.16892 kJ/min.
In order to convert the specific heat to kJ kg-1 °C, we need to use the following conversion:
1 Btu 1b-1°F = 1055.06 J kg-1 °C
Since 1 Btu = 1.05506 kJ, the specific heat in kJ kg-1 °C is 0.9 * 1.05506
= 0.94955 kJ kg-1 °C.
To determine the rate of heating in kJ S-1, we need to calculate the heat energy transferred in unit time. The heat energy transferred can be found using the formula:
Q = mcΔT
where Q is the heat energy transferred, m is the mass of the sugar syrup, c is the specific heat, and ΔT is the change in temperature.
First, we need to calculate the mass of the sugar syrup using the density and volume:
mass = density * volume
mass = 66.9 lb/ft3 * 50 ft3
= 3345 lb
Since 1 lb = 0.45359237 kg, the mass of the sugar syrup is 3345 * 0.45359237
= 1515.736 kg.
Substituting the values into the formula, we get:
Q = 1515.736 * 0.94955 * (80 - 20)
Q = 1515.736 * 0.94955 * 60
Q = 86225.0676 kJ
Finally, we can determine the rate of heating by dividing the heat energy transferred by the time:
Rate of heating = Q / time
Rate of heating = 86225.0676 kJ / 30 min
Rate of heating = 2874.16892 kJ/min
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