Conductive heat transfer through basement wall

[omc1]

Homework Statement

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 13.8oC. The temperature at the inside surface of the wall is 20.8oC. The wall is 0.118m thick and has an area of 9.43m2. Assume one kilowatt*hour of electrical energy costs $0.10. How many hours are required for one dollar's worth of energy to be conducted through the wall?

Homework Equations

q=KAdeltaT/L

The Attempt at a Solution

(1.7)*(9.43)*(20.8-13.8)/0.118=950.99 W $1=10000Whr
10000/950.99=1052 hrs...not working though?

 

[mpreds]

Where did you find your k value? And is it in the correct units?

-Mark

PS: You did mean to write 10.52 hrs I hope?

 

[omc1]

yes i mean to write that, I got 1.7 from online source, but someone else also used 1.5 but neither of those works?

 

[mpreds]

Are you working from a textbook? Check to see if there is any data tables in the back that may contain concrete.

http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

Shows a range of 0.1 - 1.7 for concrete k values

 

[Nickie]

I would first clarify some assumptions and gather more information to accurately answer this question. Some clarifying questions I would ask are:

1. Is the basement wall made of pure concrete or are there other materials involved? Different materials have different thermal conductivities, which would affect the rate of heat transfer.

2. Is the basement wall insulated? If so, what is the insulation material and its thickness? Insulation can significantly reduce conductive heat transfer through the wall.

3. How is the electric heating system set up in the home? Is it solely for heating the basement or does it also heat other parts of the house? This information would affect the amount of energy used for heating the basement and therefore the time required for one dollar's worth of energy to be conducted through the wall.

Assuming that the wall is made of pure concrete and is not insulated, and that the electric heating system is only used for the basement, here is my attempt at a solution:

Given:
- Temperature of ground in contact with wall (T1) = 13.8oC
- Temperature at inside surface of wall (T2) = 20.8oC
- Wall thickness (L) = 0.118m
- Wall area (A) = 9.43m2
- Cost of 1 kWh = $0.10

To find:
- Time (t) required for 1 dollar's worth of energy to be conducted through the wall

Solution:
1. Calculate the temperature difference (deltaT):
deltaT = T2 - T1 = 20.8 - 13.8 = 7oC

2. Calculate the thermal conductivity of concrete (K):
According to Engineering Toolbox, the thermal conductivity of concrete ranges from 0.8 to 1.7 W/mK. For this calculation, I will use the average value of 1.25 W/mK.
K = 1.25 W/mK

3. Calculate the rate of heat transfer (q):
q = K * A * deltaT / L
q = (1.25) * (9.43) * (7) / (0.118)
q = 744.49 W

4. Calculate the energy used in one hour (E):
E = q * t
E = 744.49 * t

5. Set E equal to 1 kWh and solve for t:
1 = 744