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 2.2 cm thick on the inside wall surface. The wood has $k$ = 0.080 W/m $\cdot$ K, and the Styrofoam has $k$ = 0.027 W /m $\cdot$ K. The interior surface temperature is 19.0$^\circ$C, and the exterior surface temperature is -10.0$^\circ$C. (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

Name: Problem 59, Chapter 17: University Physics with Modern Physics
Uploaded: 2019-12-18T20:10:17-08:00
Duration: 5 min 15 s
Channel: Carlos Henrique De Lima

   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 2.2 cm thick on the inside wall surface. The wood has $k$ = 0.080 W/m $\cdot$ K, and the Styrofoam has $k$ = 0.027 W /m $\cdot$ K. The interior surface temperature is 19.0$^\circ$C, and the exterior surface temperature is -10.0$^\circ$C. (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 17, Problem 59

Instant Answer

Solved by Expert Carlos Henrique De Lima

12/18/2019

Step 1

So, we can write the heat flow in the wood (HW) and the heat flow in the Styrofoam (HS) as follows: \[HW = k_{w} \cdot A \cdot \frac{T_{1}-T}{d_{w}}\] \[HS = k_{s} \cdot A \cdot \frac{T-T_{2}}{d_{s}}\] where $k_{w}$ and $k_{s}$ are the thermal conductivities Show more…

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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 2.2 cm thick on the inside wall surface. The wood has $k$ = 0.080 W/m $\cdot$ K, and the Styrofoam has $k$ = 0.027 W /m $\cdot$ K. The interior surface temperature is 19.0$^\circ$C, and the exterior surface temperature is -10.0$^\circ$C. (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?