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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

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

  1. Sketch a graph of pressure vs. volume for this process.
  2. Calculate the work done on the gas during this process, assuming that there are no “other” types of work being done.
  3. Calculate the change in the helium’s energy content during this process.
  4. Calculate the amount of heat added to or removed from the helium during this process.
  5. Describe what you might do to cause the pressure to rise as the helium expands.

Derive the equation 1.40 from the equation 1.39

Suppose you open a bottle of perfume at one end of a room. Very roughly, how much time would pass before a person at the other end of the room could smell the perfume, if diffusion were the only transport mechanism? Do you think diffusion is the dominant transport mechanism in this situation?

Measured heat capacities of solids and liquids are almost always at constant pressure, not constant volume. To see why, estimate the pressure needed to keep Vfixed as Tincreases, as follows.

(a) First imagine slightly increasing the temperature of a material at constant pressure. Write the change in volume,dV1, in terms of dTand the thermal expansion coefficient βintroduced in Problem 1.7.

(b) Now imagine slightly compressing the material, holding its temperature fixed. Write the change in volume for this process, dV2, in terms of dPand the isothermal compressibility κT, defined as

κT≡−1V∂V∂PT

(c) Finally, imagine that you compress the material just enough in part (b) to offset the expansion in part (a). Then the ratio of dPtodTis equal to (∂P/∂T)V, since there is no net change in volume. Express this partial derivative in terms of βandκT. Then express it more abstractly in terms of the partial derivatives used to define βandκT. For the second expression you should obtain

∂P∂TV=−(∂V/∂T)P(∂V/∂P)T

This result is actually a purely mathematical relation, true for any three quantities that are related in such a way that any two determine the third.

(d) Compute β,κT,and(∂P/∂T)Vfor an ideal gas, and check that the three expressions satisfy the identity you found in part (c).

(e) For water at 25∘C,β=2.57×10−4K−1andκT=4.52×10−10Pa−1. Suppose you increase the temperature of some water from 20∘Cto30∘C. How much pressure must you apply to prevent it from expanding? Repeat the calculation for mercury, for which (at25∘C)β=1.81×10−4K−1andκT=4.04×10−11Pa−1

Given the choice, would you rather measure the heat capacities of these substances at constant vor at constant p?

A 60-kghiker wishes to climb to the summit of Mt. Ogden, an ascent of5000vertical feet(1500m) .
aAssuming that she is 25%efficient at converting chemical energy from food into mechanical work, and that essentially all the mechanical work is used to climb vertically, roughly how many bowls of corn flakes (standard serving size 1ounce,100 kilocalories) should the hiker eat before setting out?
b As the hiker climbs the mountain, three-quarters of the energy from the corn flakes is converted to thermal energy. If there were no way to dissipate this energy, by how many degrees would her body temperature increase?
cIn fact, the extra energy does not warm the hiker's body significantly; instead, it goes (mostly) into evaporating water from her skin. How many liters of water should she drink during the hike to replace the lost fluids? (At25∘C, a reasonable temperature to assume, the latent heat of vaporization of water is 580cal/gmore than atrole="math" localid="1650290792399" 100∘C).
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