Question

The figure shows heat inflow and outflow for a waste-to-energy plant furnace. Assume:
(i) total heat loss = 3% of heat released from waste,
(ii) sensible heat of waste is negligible,
(iii) complete burning of waste.
Given waste feed rate = 70 kg/h, air heat input = 300 kcal/h,
flue gas = 90000 kcal/h, ash = 10000 kcal/h.
Find the heat content of waste (kcal/kg), rounded to one decimal place.

Hint:

Always include heat losses in the furnace energy balance—here losses depend directly on heat released from the waste.

Answer 1

Correct Answer: 1467

Step 1: Heat balance for the furnace.
Let: \[ H_w = \text{heat released from waste (kcal/h)}. \] Total heat input: \[ Q_{in} = H_w + 300. \] Total heat output consists of: \[ 90000\ (\text{flue gas}) + 10000\ (\text{ash}) + \text{heat losses}. \] Step 2: Heat loss equals 3% of heat released from waste. \[ \text{Loss} = 0.03 H_w. \] Step 3: Apply energy balance. \[ H_w + 300 = 90000 + 10000 + 0.03 H_w. \] Simplify: \[ H_w + 300 = 100000 + 0.03 H_w, \] \[ H_w - 0.03 H_w = 100000 - 300, \] \[ 0.97 H_w = 99700, \] \[ H_w = \frac{99700}{0.97} = 102783.5\ \text{kcal/h}. \] Step 4: Convert to heat content per kg. \[ \text{Waste feed rate} = 70\ \text{kg/h}. \] \[ \text{Heat content per kg} = \frac{102783.5}{70} = 1468.34\ \text{kcal/kg}. \] Rounded to one decimal: \[ \boxed{1468.3\ \text{kcal/kg}} \]