Heat loss rate directionality/sign convention

[adammw111]

Homework Statement

An 8.0m by 12m house is built on a concrete slab 23cm thick. What is the heat-loss rate through the floor if the interior is at 20°C while the ground is at 10°C?

Homework Equations

[itex]H=-k A \frac{\Delta T}{\Delta x}[/itex]

k_concrete = 1.0 W / m K (approx)

The Attempt at a Solution

[itex]H=\frac{-1.0 (8 * 12) (10-20)}{0.23} = 4.17[/itex] kW

My problem is that the book (Essential University Physics, Wolfson) has the answer as -4.17 kW, but that would imply that heat is being transferred from the ground to the house, which it clearly cannot be from the temperature of the house being larger than the ground's temperature.

I usually have problems with the sign of this value of H, how do I know what direction they are asking for by "through" an object - it could be either. Would either value be acceptable in an exam?

Thanks.

 

[RTW69]

Are you sure the sign on delta X is positive? What is your coordinate system for the horizontal slab? Is x=0 the 10 or 20 C surface?

 

[technician]

First of all you have given K to be 1.0W/mK. which means 1000W/K to be used in the equation . This gives the answer to the equation to be 4.17kW.
As to which direction, heat flows from hot to cold.
Sometimes worrying about the signs that crop up in equations can be confusing... they are never 'wrong' but don't forget common sense.

 

[technician]

Sorry! My mistake, mK is correct I misread it as milliKelvin and not as m.K
Ignore my previous response

 

[asteriatic]

As a scientist, it is important to understand the sign convention and directionality when dealing with heat loss. In this case, the heat loss rate is defined as the amount of heat transferred from the house to the ground, so it should be a positive value. However, the negative sign in the calculation indicates that the heat is being lost from the ground to the house. This is due to the convention that heat transfer is considered positive when it occurs from a hotter object to a colder object.

In this case, the ground is colder than the house, so the heat transfer is considered negative. It is important to pay attention to the signs and understand the directionality in order to correctly interpret the results.

In an exam, it is important to follow the sign convention and directionality specified in the question. However, if the directionality is not specified, it is always a good idea to state your assumptions and reasoning in your answer.