Question

You are burning wood to heat water for your industrial process. What is the mass of wood required to raise the temperature of 1000 kg of water from 25.0 to 100.0 °C (in kg with at least 3 sig figs.)? The specific heat of water is 4.184 J/g°C, and the lower heating value of dry wood is 16.72 MJ/kg.

Answer 1

18,8kg of wood

Step-by-step explanation:

The energy you need to to raise the temperature of 1000 kg of water from 25.0 to 100.0 °C is:

q = C×m×ΔT

Where: q is heat, C is specific heat of water (4,184J/g°C), m is mass in grams (1000x10³g), and ΔT is 100,0°C - 25,0°C = 75,0°C

Replacing:

q = 4,184J/g°C×1000x10³g×75,0°C

q = 3,14x10⁸ J of heat are required

Now, if the heating value of dry wood is 16,72 MJ/kg = 16,72x10⁶ J/kg, mass of wood required is:

3,14x10⁸J × (1kg / 16,72x10⁶ J) = 18,8 kg of wood are required

I hope it helps!