Question

A carpenter builds an exterior house wall with a layer of wood 3.0 cm thick on the outside and a layer of Styrofoam insulation 2.4 cm thick on the inside wall surface. The wood has k=0.080W/(m?K), and the Styrofoam has k= 0.010 W/(m?K). The interior surface temperature is 20.0 ?C , and the exterior surface temperature is -13.0 ?C

A.)What is the temperature at the plane where the wood meets the Styrofoam? _______ Celsius

B.)What is the rate of heat flow per square meter through this wall? ______W/m^2

Answer 1

Answer:

Explanation:

Given

thermal conductivity of wood $K_w=0.08 W/m^2-K$

thermal conductivity of insulation $K_i=0.01 W/m^2-K$

thickness of wood $t_2=3 cm$

thickness of insulation $t_1=2.4 cm$

$T_i=20^{\circ}C$

$T_o=-13^{\circ}C$

we know heat Flow is given by

$Q=kA\frac{dT}{dx}$

$dT=$ change in temperature

$dx=$ thickness

K=thermal conductivity

A=Area of cross-section

A is same

Suppose T is the temperature of Junction

as heat Flow is same thus

$\frac{k_w(20-T)}{3}=\frac{k_i(T-(-13))}{2.4}  $      

$\frac{0.08(20-T)}{3}=\frac{0.01(T+13)}{2.4}$

$T=19.36 ^{\circ}C$

(b)Rate of heat flow

$Q=\frac{k_w(T+13)}{3\times 10^{-2}}$

$Q=\frac{0.08\times 32.36}{0.03}$

$Q=86.303 W/m^2$