Question

you are living by the beach and have decided to build a concrete home. It is typically air conditioned as 20 C, while the outside temperature is 97 C on average. For a home with dimensions as shown below and 0.2m thick walls, what is the typical daily energy loss of the home due to cooling the heat transferring into the home through concrete if the thermal conductivity of concrete is k=1.4 W/m K. Answer in mWh   

Dimensions 10 by 15 by 6

Answer 1

Hi,

Hope you are doing well.

STEP 1:

We know that the energy lost daily is given as the heat transferred to the the home from outside, since there is a temperature difference.
We know that there will be 4 walls (2 with same area) for a typical home.

Given that,

Temperature difference between room and outside,

(temperature difference will be same in ^oC and Kelvin scale).

Thickness of the concrete walls,

Thermal conductivity of concrete,

STEP 2:

There will be two walls with same area.

Hence area of first and opposite wall is given by,

Similarly, area of the second wall and it;s opposite wall will be,

STEP 3:

We know that, Amount of heat transferred is given by,

Where is the time taken.

Here we are asked to find daily heat loss. Hence time taken will be 24 hours.

STEP 4:

Hence, Heat transfer through the first wall is given by,

Heat transfer through the first wall's opposite wall will be also the same(since area is same).

Heat transfer through the second wall is given by,

Heat transfer through the second wall's opposite wall will be also the same (since area is same).

STEP 5:

Hence total daily energy loss is given by,

STEP 6:

We know that,

Rounding to 3 significant figures,