Question

Burning 1.0 kg of anthracite coal releases 30,500 kJ of heat. Calculate the mass of coal required to heat 4.0 kg of water from 20ºC to its boiling point of 100ºC. (Specific heat capacity of water = 4.184 J/g°C)

A. 26.4 g
B. 112 g
C. 43.9 g
D. 37.1 g
E. 72.7 g
F. 16.2 g

Answer 1

C. 43.9 g

Step-by-step explanation:

The formula for calculating the heating of the water:

Q = m * C * ΔT

Where Q is the amount of heat required, m is the mass of the object, C is the specific heat capacity of the material, and ΔT is the change in temperature. Plugging in the values from the problem, we get the following:

Q = 4000 g * 4.184 J/g°C * (100°C - 20°C) = 1,338,880 J = 1338.88 kJ

The mass of anthracite coal required:

`m_(coal)` = 1338.88 kJ / 30,500 kJ/kg = 0.0439 kg = 43.9 g