A single-effect evaporator evaporates water from clarified fruit juice at an evaporation rate of $V = 1500\text{ kg/h}$ (latent heat $\lambda_v = 2257\text{ kJ/kg}$). Dry saturated steam at $120.0^\circ\text{C}$ (latent heat $\lambda_s = 2200\text{ kJ/kg}$) is supplied at a mass flow rate of $S = 1800\text{ kg/h}$. The steam economy of the evaporator ($\text{Economy} = \frac{V}{S}$) is ________ (round off to two decimal places).
Answer Key:
0.83
Step-by-Step Solution & Explanation
Multi-Approach Solution:
**Method 1: Direct Ratio Definition**
Steam economy is the mass of vapor produced per unit mass of live steam consumed:
$\text{Steam Economy} = \frac{V}{S} = \frac{1500\text{ kg/h}}{1800\text{ kg/h}} = \frac{15}{18} = \frac{5}{6} \approx 0.8333 \approx 0.83$
**Method 2: Enthalpy Energy Check**
Energy utilized for evaporation: $q_{\text{evap}} = 1500 \times 2257 = 3.3855 \times 10^6\text{ kJ/h}$.
Energy supplied by condensing steam: $q_{\text{steam}} = 1800 \times 2200 = 3.960 \times 10^6\text{ kJ/h}$.
Thermal efficiency $\eta = \frac{3.3855}{3.960} = 85.5\%$. Economy remains $\frac{V}{S} = 0.83$.