Question

|| A 10 m$\times$14 m house is built on a 12-cm-thick concrete slab.

What is the heat-loss rate through the slab if the ground temperature

is 5$°$C while the interior of the house is 22$°$C?

Short answer

The power needed is 15.9 kW

Step-by-step solution

Formula to use in this problem

For thermal conduction,

$\frac{dQ}{dt}=\frac{kA}{L}∆T$,

where dQ is the heat transferred in dt and dt is the time differential. If the time difference is unit,$P=\frac{dQ}{dt}$

Rearrangement of the equation and finding of the power needed

As our surface is rectangular, A=ab, where a and b are the dimensions of the floor. So,

$P=\frac{kab∆T}{L}=\frac{0.8·10·14·(22-5)}{0.12}=1.59·{10}^4=15.9kW$