Reference ID: MET-9B30 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The specific heat of sugar solutions governs how much energy is required to heat or cool syrups, juices, and molasses in food, beverage, and bio-refining plants. Knowing this value lets process engineers size heat exchangers, evaporators, sterilizers, and storage tanks without over-designing utility loads. Because dissolved sucrose lowers the specific heat of water in a predictable way, a simple correlation is often sufficient for preliminary equipment specification and energy budgeting.
Methodology & Formulas
Step 1 – Temperature Driving Force
The temperature change across the process is
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]
Step 2 – Solution Specific Heat
Dissolved sugar reduces the specific heat of water through a linear correction:
\[ c_{p,\text{solution}} = c_{p,\text{water}} \left(1 - f\,x_{\text{sugar}}\right) \]
where
\( c_{p,\text{water}} \) is the specific heat of pure water at the working temperature,
\( f \) is an empirical factor (dimensionless) fitted to sucrose–water data,
\( x_{\text{sugar}} \) is the mass fraction of dissolved sugar (dry basis).
Step 3 – Energy Requirement
The total sensible heat load is obtained from
\[ Q = m\,c_{p,\text{solution}}\,\Delta T \]
with \( m \) the total mass of solution to be heated or cooled.
Parameter
Symbol
Unit
Typical Range
Mass fraction sugar
\( x_{\text{sugar}} \)
kg kg-1
0–0.65
Empirical factor
\( f \)
—
0.66 (sucrose)
Specific heat water
\( c_{p,\text{water}} \)
kJ kg-1 °C-1
4.18 @ 20 °C
A quick field estimate for 0–65 °Brix at 20–80 °C is
cp ≈ 4.19 – 0.033 · Brix (kJ kg-1 °C-1)
For design work use the more rigorous Chen–Joshi correlation:
cp = 4.186 (1 – 0.0078 Brix) – 0.002 (T – 20)
where T is in °C. This keeps the error within ±2 % up to 70 °Brix.
0–70 °Brix: direct use with <2 % error.
70–78 °Brix: add a +1 % correction to the predicted value to compensate for non-ideal behaviour.
>78 °Brix: switch to a mass-fraction based model or experimental data; predictions diverge rapidly.
Yes. Between 60 °C and 120 °C the specific heat of a 60 °Brix solution drops by roughly 3 %. If your evaporator stages operate across this span, apply the temperature term in the Chen–Joshi equation or allow ±1 % safety margin on heat-transfer coefficients.
Invert sugar at the same °Brix lowers cp by 0.5–1 % because of its lower water activity.
Typical cane juice ash (1–1.5 % ds) raises cp by ~0.3 %; beet thin juice with 2 % salts can raise it by 0.6 %.
For mixed juices use a weighted average: cp,blend = Σ (mi cp,i) / Σ mi.
Cool a 500 g sample from 85 °C to 45 °C in a jacketed lab vessel with known coolant flow.
Measure ΔT and flow to obtain Q.
Calculate cp = Q / (m · ΔTsample).
Compare with predicted; repeat at two Brix levels. Deviations >3 % indicate either measurement error or non-ideal behaviour beyond the model range.
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Worked Example – Specific Heat of a 45 wt % Sugar Solution
A beverage plant needs to heat 800 kg of 45 wt % sucrose solution from 15 °C to 85 °C for pasteurisation. The process engineer must predict the specific heat of the solution and the total energy required.
Knowns
Mass of solution, m = 800 kg
Mass fraction sugar, xsugar = 0.45
Inlet temperature, T1 = 15 °C
Outlet temperature, T2 = 85 °C
Temperature rise, ΔT = 70 °C
Specific heat of pure water at 50 °C, Cp,water = 4.18 kJ kg⁻¹ °C⁻¹
Empirical sugar-reduction factor, F = 0.66
Step-by-step calculation
Estimate the solution specific heat using the mass-weighted mixing rule:
\[ c_{p,\text{solution}} = C_{p,\text{water}} \left[1 - (1 - F)\,x_{\text{sugar}}\right] \]
Insert the known values:
\[ c_{p,\text{solution}} = 4.18 \left[1 - (1 - 0.66)(0.45)\right] \]
