Heat moving through the walls of a house

[Punkyc7]

A carpenter builds an exterior house wall with a layer of wood 3.2 {\rm cm} thick on the outside and a layer of Styrofoam insulation 2.4 cm thick on the inside wall surface. The wood has k=0.080 W/(m* K, and the Styrofoam has k= 0.010 W/ m* K)}. The interior surface temperature is 20.0C, and the exterior surface temperature is -12.0C.

What is the temperature at the plane where the wood meets the Styrofoam?


so i set up

H=Ak(Tf-T0)/L

H=Ak(Tf-T0)/L

set them both equal so the A drops out

.08(x-20)/.o32=.01(x+12)/.024

and get 26.4 which is wrong, so where am i going wrong at?

 

[PeterO]

A carpenter builds an exterior house wall with a layer of wood 3.2 {\rm cm} thick on the outside and a layer of Styrofoam insulation 2.4 cm thick on the inside wall surface. The wood has k=0.080 W/(m* K, and the Styrofoam has k= 0.010 W/ m* K)}. The interior surface temperature is 20.0C, and the exterior surface temperature is -12.0C.

What is the temperature at the plane where the wood meets the Styrofoam?


so i set up

H=Ak(Tf-T0)/L

H=Ak(Tf-T0)/L

set them both equal so the A drops out

.08(x-20)/.o32=.01(x+12)/.024

and get 26.4 which is wrong, so where am i going wrong at?

Your temperature difference on the LHS is wrong way round.

x will be between 20 and -12, so the temp differences should be 20 - T, and T - (-12)

Hopefully that fixes it up.