Answer :
the temperature change in a garage due to incandescent lighting can be calculated using the given equation and information regarding bulb power, power lost as heat, and time of operation.
total bulb power = no. of bulbs × bulb power
= 6 × 60 = 360W
total bulb power lost = (total bulb power × percentage power lost as heat)/100
= 360 × 90/100 = 324W
Total Bulb Energy Lost as Heat over 3 hours:
total bulb energy lost as heat = 324×3 hrs= 972 W
find mass of air = 5760 [tex]ft^3[/tex]× 1.2 = 6912 kg
temperature change = (972×3600) / (6912×1000)= 0.1406 K
therefore, the temperature in the garage would increase by approximately 0.1406 K due to the light bulbs being on for 3 hours.
Total Bulb Power: 360 W
Total Bulb Power Lost as Heat: 324 W
Total Bulb Energy Lost as Heat: 972 Wh
Garage Air Mass: 6912 kg
Temperature Change: 0.1406 K
To calculate the temperature change in the garage due to the light bulbs, we can follow these steps:
1. Calculate the total power consumed by all bulbs.
2. Calculate the total power lost as heat by all bulbs.
3. Calculate the total energy lost as heat by all bulbs over the 3 hours.
4. Determine the mass of the air in the garage.
5. Calculate the temperature change using the formula provided.
Let's proceed with the calculations:
1. Total Bulb Power:
[tex]\[ \text{Total Bulb Power} = \text{Number of Bulbs} \times \text{Bulb Power} \][/tex]
[tex]\[ = 6 \times 60 \text{ W} = 360 \text{ W} \][/tex]
2. Total Bulb Power Lost as Heat:
[tex]\[ \text{Total Bulb Power Lost as Heat} = \text{Total Bulb Power} \times \left( \frac{\text{Percent Power Lost as Heat}}{100} \right) \][/tex]
[tex]\[ = 360 \text{ W} \times \left( \frac{90}{100} \right) = 324 \text{ W} \][/tex]
3. Total Bulb Energy Lost as Heat over 3 hours:
[tex]\[ \text{Total Bulb Energy Lost as Heat} = \text{Total Bulb Power Lost as Heat} \times \text{Bulbs on Time} \][/tex]
[tex]\[ = 324 \text{ W} \times 3 \text{ hrs} = 972 \text{ Wh} \][/tex]
4. Determine the mass of the air in the garage:
[tex]\[ \text{Garage Air Mass} = \text{Garage Air Volume} \times \text{Air Density} \][/tex]
[tex]\[ = 5760 \text{ ft}^3 \times 1.2 \text{ kg/m}^3 \][/tex]
[tex]\[ = 6912 \text{ kg} \][/tex]
5. Calculate the temperature change:
[tex]\[ \text{Temperature Change} = \frac{\text{Total Bulb Energy Lost as Heat}}{\text{Garage Air Mass} \times \text{Air Heat Capacity}} \][/tex]
[tex]\[ = \frac{972 \text{ Wh} \times 3600 \text{ s/hr}}{6912 \text{ kg} \times 1000 \text{ J/kg K}} \][/tex]
[tex]\[ \approx 0.1406 \text{ K} \][/tex]
So, the temperature in the garage would increase by approximately 0.1406 K due to the light bulbs being on for 3 hours.