Question

Chapter 13, Problem 01

The amount of heat per second conducted from the blood capillaries beneath the skin to the surface is 280 J/s. The energy is transferred a distance of 2.1 × 10^-3 m through a body whose surface area is 1.8 m². Assuming that the thermal conductivity is that of body fat, determine the temperature difference between the capillaries and the surface of the skin.

Chapter 13, Problem 02

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.4 ^oC. The temperature at the inside surface of the wall is 20.8 ^oC. The wall is 0.11 m thick and has an area of 8.2 m². Assume that one kilowatt hour of electrical energy costs $0.10. How many hours are required for one dollar's worth of energy to be conducted through the wall?

Answer 1

1) Thermal conduction:

The transfer of heat between two objects in contact with each other is called thermal conduction.

There are four factors that affect the rate of thermal conduction: K,A , and d.

where K= thermal conductivity constant for the material

A = cross sectional area of the material

  = temperature difference between one side of the material and the other

d= thickness of the material

Rate of thermal conduction is given by the equation:

Given:

Rate of thermal conduction,Q/t= 280 J/s

Thickness of material,d = 2.1 *10^-3 m

Cross sectional area,A= 1.8 m²

Thermal conductivity constant, k= 0.2 J/sm⁰C ( thermal conductivity is of body fat)

Substituting the given values in our equation,

Therefore ,the temperature difference between the capilleries and the surface of the skin is 1.63 ⁰C