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

Provided: Room dimensions = 12 m × 8 m, height = 4 m; Combustible material volume = 80 m\(^3\); Combustible material density = 3.0 kg/m\(^3\); Calorific value = 4000 kcal/kg.
\n\nStep 1: Calculate the total mass of the combustible material.
\n\[\n{Mass} = {Density} \times {Volume} = 3.0 \, {kg/m}^3 \times 80 \, {m}^3 = 240 \, {kg}\n\]\n\nStep 2: Calculate the total calorific value.
\n\[\n{Total calorific value} = {Mass} \times {Calorific value} = 240 \, {kg} \times 4000 \, {kcal/kg} = 960,000 \, {kcal}\n\]\n\nStep 3: Calculate the area of the room.
\n\[\n{Area} = 12 \, {m} \times 8 \, {m} = 96 \, {m}^2\n\]\n\nStep 4: Calculate the fire load by dividing the total calorific value by the room's area.
\n\[\n{Fire load} = \frac{{Total calorific value}}{{Area}} = \frac{960,000 \, {kcal}}{96 \, {m}^2} = 10,000 \, {kcal/m}^2\n\]\n\nThe fire load of the room is 10,000 kcal/m².