College

**1.3 Temperature Increase due to Incandescent Lighting**

When energy is added to a fluid, the temperature of the fluid increases. An equation describing this phenomenon is:

\[ Q = M C \Delta T \]

Where:
- \( Q \) is the amount of energy added (joules)
- \( M \) is the mass of the fluid (kg)
- \( C \) is the heat capacity of the fluid (joules/kg·K)
- \( \Delta T \) is the change in temperature (K, or °C)

A garage (24 ft x 24 ft x 10 ft) is illuminated by six 60W incandescent bulbs. It is estimated that 90% of the energy to an incandescent bulb is dissipated as heat. If the bulbs are on for 3 hours, how much would the temperature in the garage increase because of the light bulbs (assuming no energy losses)?

Complete an Excel worksheet like the one illustrated in Figure 1.71 to answer this question.

### Specified Information
- Number of Bulbs: 6
- Bulb Power: 60 W
- Bulb Percent Power Lost as Heat: 90%
- Bulbs on Time: 3 hrs
- Garage Air Volume: 5760 ft³
- Air Density: 1.2 kg/m³
- Air Heat Capacity: 1000 joules/kg·K

**Useful Information**
- Air density: 1.2 kg/m³
- Air heat capacity: 1000 joules/kg·K
- Length conversion: 3.28 ft = 1 m

### Calculated Information
- Total Bulb Power:
- Total Bulb Power Lost as Heat:
- Total Bulb Power Lost as Heat (joules/second):
- Total Bulb Energy Lost as Heat (joules):
- Garage Air Volume (m³):
- Garage Air Mass (kg):
- Temperature Change (K):

### Hints:
- Consider the number of bulbs.
- Consider the total bulb power and percent power lost.
- Convert the time units.
- Unit conversion (volume * density).
- Energy lost divided by (air mass * air heat capacity).

Complete the table to determine the temperature change in the garage due to the incandescent lighting.

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.