Question

Styrofoam, used for insulation, has a thickness of 25.0 mm . The temperature on one side of the styrofoam wall is 12.0 0C and 22.5 0C on the other side. How much heat (J) is transferred in one hour through each square meter of the styrofoam wall to 3 sig figs? In real construction there will be bricks or concrete along with the styrofaom as you can see in the picture. Only consider the styrofoam here.

Answer 1

Given,

Thickness is

$d=25.0mm$

The temperatures are:

$\begin{gathered} T_1=12.0^oC \\ T_2=22.5^oC \end{gathered}$

The time taken is

$t=1hr=3600\text{ sec}$

To find

Heat (J) transferred in one hour through each square meter of the styrofoam wall.

Explanation:

Let Q be the heat transferred

We know, the thermal conductivity of styrofoam is

$k=0.033\text{ W/mK}$

Now rate of heat transfer through conduction is:

$\begin{gathered} \frac{Q}{t}=kA\frac{(T_2-T_1)}{d} \\ \Rightarrow\frac{Q}{3600}=0.033\times1\times\frac{(22.5-12)}{25\times10^{-3}} \\ \Rightarrow Q=49896\text{ J} \end{gathered}$

Conclusion

The required answer is 49896 J.