Question

A room having dimension of 12 m × 8 m and height 4 m, stores a certain combustible material of volume 80 m\(^3\). The density and calorific value of the combustible material are 3.0 kg/m\(^3\) and 4000 kcal/kg, respectively. The fire load of the room is _________ kcal/m\(^2\). (rounded off to the nearest integer)

Hint:

When calculating fire load, remember to use the correct units for density, volume, and calorific value to obtain the correct results.

Answer 1

Given:
Dimensions of the room = 12 m × 8 m and height = 4 m
Volume of the combustible material = 80 m\(^3\)
Density of the combustible material = 3.0 kg/m\(^3\)
Calorific value = 4000 kcal/kg
Step 1: The total mass of the combustible material is given by: \[ {Mass} = {Density} \times {Volume} = 3.0 \, {kg/m}^3 \times 80 \, {m}^3 = 240 \, {kg} \] Step 2: The total calorific value is the mass of the material multiplied by its calorific value: \[ {Total calorific value} = {Mass} \times {Calorific value} = 240 \, {kg} \times 4000 \, {kcal/kg} = 960,000 \, {kcal} \] Step 3: The area of the room is given by: \[ {Area} = 12 \, {m} \times 8 \, {m} = 96 \, {m}^2 \] Step 4: The fire load is calculated as the total calorific value divided by the area of the room: \[ {Fire load} = \frac{{Total calorific value}}{{Area}} = \frac{960,000 \, {kcal}}{96 \, {m}^2} = 10,000 \, {kcal/m}^2 \] Thus, the fire load of the room is 10,000 kcal/m².