Calculate Heat Flow Rate Across a Wall: 100 W Lightbulbs

In summary, the problem involves two rooms with a 12 cm thick brick wall between them. One room has a temperature of 27°C due to 100 W light-bulbs, while the other room is at 10°C. To maintain this temperature difference, we need to round up to 17 of the 100 W light-bulbs.
  • #1
electritron
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Homework Statement



Two rooms, each a cube 3.8 m on a side, share a 12 cm thick brick wall. Because of a number of 100 W light-bulbs in one room, the air is at 27°C, while in the other room it is at 10°C. How many of the 100 W light-bulbs are needed to maintain the temperature difference across the wall? (Round your answer up to the nearest integer.)

Homework Equations



Q/t=kA(t1-t2)/l

The Attempt at a Solution



This looks so easy and I attempt to solve it and I get it wrong.
I used
Q/t=kA(t1-t2)/l
=(0.84J/s*m*C)(14.44m2)(27C-17C) / (0.12m)
=1718.36 then divide by 100 and it equals 17.1836=17
Do you have any ideas as to what I'm not comprehending because I'm sure this has to be the correct number of bulbs.
 
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  • #2
Welcome to PF :smile:

The instructions say to round the answer up. Otherwise things look fine (assuming k is correct).
 

1. How do I calculate the heat flow rate across a wall with 100 W lightbulbs?

To calculate the heat flow rate, you will need to know the thermal conductivity of the wall material, the surface area of the wall, and the temperature difference between the two sides of the wall. You can then use the formula Q = kA∆T, where Q is the heat flow rate, k is the thermal conductivity, A is the surface area, and ∆T is the temperature difference.

2. What is the thermal conductivity of a typical wall material?

The thermal conductivity of a wall material can vary depending on the type of material. However, a typical value for a common wall material like brick or drywall is around 0.5 - 1.5 W/mK.

3. How do I determine the surface area of the wall?

To determine the surface area of the wall, you will need to measure the length and width of the wall and then calculate the area by multiplying the two measurements. If the wall has irregular shapes, you may need to break it down into smaller sections and calculate the area for each section separately.

4. What is considered a high heat flow rate for a wall?

The heat flow rate across a wall can vary depending on the specific situation. However, a high heat flow rate is typically considered to be anything above 10 W/m2. If the heat flow rate is significantly higher than this, it may indicate a need for better insulation or other measures to reduce heat transfer.

5. Can I use this formula for calculating heat flow rate across a wall for other types of heat sources?

Yes, this formula can be used for calculating the heat flow rate across a wall for any type of heat source, not just 100 W lightbulbs. However, keep in mind that the thermal conductivity and surface area may vary depending on the type of heat source and the material of the wall.

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