152
Temperature and Heat Table 10.2
Conversions Related to Heat Energy
1 Btu = 252 cal 1 Btu = 1,055J 1 Btu = 778 ft·lb 1 cal = 4.19J 1 ft·lb = 0.324 cal 1 ft·lb = 1.355J
1 cal = 0.0039 Btu 1J = 0.000948 Btu 1 ft·lb = 0.001285 Btu 1J = 0.239 cal 1J = 0.738 ft·lb 1W = 1 J/s
W TH =
3 kT 2
(10.5) −23
where k = Boltzmann’s constant = 1.38 × 10 J/K. The above also can be used to determine the average velocity vTH of a gas molecule from the kinetic energy equation: W TH =
1 3 2 mν TH = kT 2 2
from which ν TH =
3kT m
(10.6)
where m is the mass of the molecule in kilograms. Example 10.4
What is the average thermal speed of an oxygen atom at 320°R? The molecular mass of oxygen is 26.7 × 10−27 kg. 320°R = 320 × 5/9K = 177.8K ν TH =
ν TH =
3kT m
3 × 138 . × 10 −23 J K × 177.8K × 267 . × 10 −27 kg
kg × m 2 s2 × J
ν TH = 525 m s
The specific heat of a material is the quantity of heat energy required to raise the temperature of a given weight of the material 1°. For example, as already defined, 1 Btu is the heat required to raise 1 lb of pure water 1°F, and 1 cal is the heat required to raise 1g of pure water 1°C. Thus, if a material has a specific heat of 0.7 cal/g °C, then it would require 0.7 cal to raise the temperature of a gram of the material 1°C, or 2.93J to raise the temperature of the material 1K. Table 10.3 gives the specific heat of some common materials, in which the values are the same in either system.