Question

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

1.877 x 10⁷ kg

Step-by-step explanation:

To solve this problem we first use the equation:

• Q = m * c * ΔT

Where Q is the heat needed to increase the temperature of a substance, m is the mass, c is the specific heat and ΔT is the difference in temperature.

For this problem:

• m = 1000 kg = 1000000 g

• J = 4.184 J/g°C

• ΔT = 100°C - 25°C = 75°C

We put the data in the equation and solve for Q:

• Q = 1000000 g * 4.184 J/g°C * 75°C

• Q = 313.80 MJ

So that's the energy required to heat 1000 kg of water, now we calculate the mass of wood using the equation:

• Q = m * b

Where b is the heating value of wood and m its mass:

• 313.80 MJ = m * 16.72 MJ/kg

• m = 1.877 x 10⁷ kg wood