Unit 44: Heat Conduction
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q44.1) Consider a wall of a house that’s 6m wide, 2.5m tall, and 10cm thick. How much heat is lost through the wall in 24 hours on a cold Winter’s day where the outside temperature is -20°C and the inside temperature is 23°C? The thermal conductivity of the wall is 0.15 W/m/°C.
**Q44.2) Two warm spheres of the same internal temperature are immersed in a bucket full of cold water. One of the spheres has three-times the radius of the other, and the smaller sphere has twice the thermal conductivity of the larger sphere. What’s the ratio of the larger sphere’s initial rate of heat loss to that of the smaller sphere?
***Q44.3) Consider the wall of a house that’s 6m wide and 2.5m tall. The wall is made of two layers: an outer layer made of 8cm of wood (thermal conductivity 0.20 W/m/°C) and an inner layer made of 2cm of insulation (thermal conductivity 0.02 W/m/°C). On a cold Winter’s day where the outside temperature is -20°C and the inside temperature is 23°C,
a) What’s the temperature at the wood/insulation interface?
b) What’s the rate of heat loss through the wall?