Answer to Question #249817 in Molecular Physics | Thermodynamics for hassan

Question

The power of the heat fan is 2.00 kW. How much coal should be burned per hour to produce the corresponding heat when the calorific value of the coal is 28.4 MJ/kg?

Answer 1

Power of 1W is equal to 1J in 1s. Thus, in one hour (3600 seconds) the coal should suplement the following amount of energy:

$$Q = 2\times 10^3\dfrac{J}{s}\cdot 3600s = 7.2\times 10^6J = 7.2MJ$$

The mass of coal is given as follows:

$$m = \dfrac{Q}{q}$$

where $q = 28.4MJ/kg$ is the calorific value of the coal. Thus, obtain:

$$m = \dfrac{7.2MJ}{28.4MJ/kg} \approx 0.253kg$$

Answer. 0.253 kg.