Answer :
A- The specific heat of the sugar syrup can be converted to 2,060 kJ/kg·°C, and
b- the rate of heating, which is the heat energy transferred per unit time, is approximately 156.96054 kJ/s in SI units.
A- To convert the specific heat from Btul⁻¹F⁻¹ to kJkg⁻¹°C⁻¹, we use the conversion factor: 1 Btul⁻¹F⁻¹ = 4.184 kJkg⁻¹°C⁻¹.
Specific heat of the sugar syrup = 0.9 Btul⁻¹F⁻¹.
Converting to kJkg⁻¹°C⁻¹:
Specific heat = 0.9 Btul⁻¹F⁻¹ * 4.184 kJkg⁻¹°C⁻¹/Btul⁻¹F⁻¹
Specific heat ≈ 3.7584 kJkg⁻¹°C⁻¹.
(b) The rate of heating, or the heat energy transferred per unit time, can be calculated using the formula:
Rate of heating = (mass of the syrup) × (specific heat) × (temperature change) / (time)
The mass of the syrup can be calculated using the volume and density:
Mass = (volume) × (density) = 50 ft³ × 66.9 lb/ft³ ≈ 3345 lb ≈ 1516.05 kg.
The temperature change is ΔT = 80°C - 20°C = 60°C.
Plugging these values into the formula, we get:
Rate of heating = (1516.05 kg) × (0.388 kJ/(kg⋅°C)) × (60°C) / (30 min × 60 s/min) ≈ 156.96054 kJ/s.
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