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Chapter 1: Q. 1.58 (page 40)

According to a standard reference table, the R value of a 3.5 inch-thick vertical air space (within a wall) is 1.0 R in English units), while the R value of a 3.5-inch thickness of fiberglass batting is 10.9. Calculate the R value of a 3.5-inch thickness of still air, then discuss whether these two numbers are reasonable. (Hint: These reference values include the effects of convection.)

Short Answer

Expert verified

The value of 3.5 inch thickness of still air is Rair= 0.176 m2. oK.s.J-1

Step by step solution

01

To Calculate R

Rvalue is,

R=Δkkt

For

localid="1651328451771" airkt=0.026Wm-1k-1

So,

3.5inch=3.5×25.6mm

=89.6×10-3m

Rair=89.6×10-3m0.026Wm-1K-1

=3.45ω-1m2k

02

After conversion.

Then,

Rair=3.450.58role="math" localid="1651327954414" offt2hr/btu

Rair=5.95role="math" offt2hr/btu

As a result, the value does not match the reference value (f=1).

Because of the convection process, reference values incorporate the impacts of convection.

The air's thermal conductivity rises.

As a result, the value of Rdecreases.

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Most popular questions from this chapter

Geologists measure conductive heat flow out of the earth by drilling holes (a few hundred meters deep) and measuring the temperature as a function of depth. Suppose that in a certain location the temperature increases by20∘Cper kilometer of depth and the thermal conductivity of the rock is 2.5W/m⋅K. What is the rate of heat conduction per square meter in this location? Assuming that this value is typical of other locations over all of the earth's surface, at approximately what rate is the earth losing heat via conduction? (The radius of the earth is 6400km.)

Imagine some helium in a cylinder with an initial volume of 1litreand an initial pressure of 1atm.Somehow the helium is made to expand to a final volume of 3litres,in such a way that its pressure rises in direct proportion to its volume.

(a) Sketch a graph of pressure vs. volume for this process.

(b) Calculate the work done on the gas during this process, assuming that there are no "other" types of work being done.

(c) Calculate the change in the helium's energy content during this process.

(d) Calculate the amount of heat added to or removed from the helium during this process.

(e) Describe what you might do to cause the pressure to rise as the helium expands.

Give an example of a process in which no heat is added to a system, but its temperature increases. Then give an example of the opposite: a process in which heat is added to a system but its temperature does not change.

Put a few spoonfuls of water into a bottle with a tight lid. Make sure everything is at room temperature, measuring the temperature of the water with a thermometer to make sure. Now close the bottle and shake it as hard as you can for several minutes. When you're exhausted and ready to drop, shake it for several minutes more. Then measure the temperature again. Make a rough calculation of the expected temperature change, and compare.

Problem 1.41. To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible.

  1. How much heat is lost by the water?
  2. How much heat is gained by the metal?
  3. What is the heat capacity of this chunk of metal?
  4. If the mass of the chunk of metal is 100 g, what is its specific heat capacity?
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