YOURSELF (Answers, p. 656)
3.5 TEMPERATURE
g
6 3
1 100
f b
f b
f b
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T T
T T
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T T
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(a) (b) (c) 4.
resistance thermometer
thermocouple pyrometer
thermometer
degree
Kelvin Rankine
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⫺ True or false?
An open-end manometer provides a direct reading of the gauge pressure of a gas.
A sealed-end manometer provides a direct reading of the absolute pressure of a gas, provided that the gas pressure in the sealed end may be neglected.
The reading of a differential manometer does not depend on the density of the fluid in the pipeline but only on that of the manometer fluid.
The pressure of a gas in a pipeline is measured with an open-end mercury manometer.
The mercury level in the arm connected to the line is 14 mm than the level in the open arm. What is the gauge pressure of the gas in the line?
Think of several devices that might be used to measure fluid pressures, being as imaginative as you can. ( Allow a gas at the pressure to be measured to fill a calibrated balloon, and measure the final balloon diameter.)
The temperature of a substance in a particular state of aggregation (solid, liquid, or gas) is a measure of the average kinetic energy possessed by the substance molecules. Since this en- ergy cannot be measured directly, the temperature must be determined indirectly by measuring some physical property of the substance whose value depends on temperature in a known man- ner. Such properties and the temperature-measuring devices based on them include electrical resistance of a conductor ( ), voltage at the junction of two dissimilar metals ( ), spectra of emitted radiation ( ), and volume of a fixed mass
of fluid ( ).
Temperature scales can be defined in terms of any of these properties, or in terms of phys- ical phenomena, such as freezing and boiling, that take place at fixed temperatures and pres- sures. You might refer, for example, to “the temperature at which the resistivity of a copper wire is 1 92 10 ohms/cm ” or to “the temperature two-thirds of the way from the boiling point of water at 1 atm to the melting point of NaCl.”
It is convenient to have, in addition to these physical scales, a simple numerical tempera- ture scale—among other reasons, so that you do not have to use 25 words to give the value of a single temperature. A defined temperature scale is obtained by arbitrarily assigning numerical values to two reproducibly measurable temperatures; for example, assign a value of 0 to the freezing point of water and a value of 100 to the boiling point of water at 1 atm. The assigned values completely specify the scale, since in addition to locating the two points they specify that the length of a unit temperature interval (called a ) is of the distance between the two reference points on the scale.
The two most common temperature scales are defined using the freezing point ( ) and boiling point ( ) of water at a pressure of 1 atm.
is assigned a value of 0 C, and is assigned a value of 100 C.
(theoretically the lowest temperature attainable in nature) on this scale falls at 273 15 C.
is assigned a value of 32 F, and is assigned a value of 212 F. Absolute zero falls at 459 67 F.
The and scales are defined such that absolute zero has a value of 0 and the size of a degree is the same as a Celsius degree (Kelvin scale) or a Fahrenheit degree (Rankine scale).
a b
a b
A de ree is both a temperature and a temperature inter al, EXAMPLE 3.5-1 Deri ation of a Temperature Con ersion Formula
SOLUTION
T T T T
T aT b
T a b b
T a a .
T . T
1 2
1
2
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⳱ Ⳮ ⳱
⳱ Ⳮ ⳱
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1 2
1 1
2 2
T T .
T T .
T . T
T . T
y ax b A
B T B
T A T T
T B aT A b
T B T A
T B T A
. .
T T T T
Derive Equation 3.5-4 for ( F) in terms of ( C). Use 0 C (32 F) and 100 C (212 F).
( F) ( C)
Substitute : 32 ( )(0) 32
Substitute : 212 ( )(100) 32 1 8
( F) 1 8 ( C) 32
(3.5-1) (3.5-2) (3.5-3) (3.5-4)
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2.
(3.5-5)
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The following relationships may be used to convert a temperature expressed in one defined scale unit to its equivalent in another:
(K) ( C) 273 15 ( R) ( F) 459 67 ( R) 1 8 (K)
( F) 1 8 ( C) 32
Equations like these always have the form of the equation of a line ( ). If ( ) and ( ) stand for any two temperature units, to derive the equation for ( ) in terms of ( ) you must know equivalent values on each scale of two temperatures—say, and . Then
Write ( ) ( )
Substitute ( ) and ( ) in the equation—you then have one equation in two un- knowns ( and ). Substitute ( ) and ( ) to get the second equation in the two unknowns, and solve for and .
a fact that sometimes leads to confusion. Consider the temperature interval from 0 C to 5 C. There are nine Fahrenheit and nine Rankine degrees in this interval, and only five Celsius degrees and five Kelvin. An interval of 1 Celsius degree or Kelvin therefore contains 1.8 Fahrenheit or Rankine degrees, leading to the conversion factors
1 8 F 1 8 R 1 F 1 C
, , ,
1 K 1 K
1 C 1 R
( C) 0 1 2 3 4 5
(K) 273 274 275 276 277 278
( F) 32 33 34 35 36 37 38 39 40 41
( R) 492 493 494 495 496 497 498 499 500 501
T(°C) =
A temperature A temperature interval
1°C 32°F
1.8°F
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These con ersion factors refer to temperature inter als, not temperatures.
EXAMPLE 3.5-2 Temperature Con ersion
SOLUTION
Note:
TEST
YOURSELF (Answers, p. 656)
T T
.
T .
.
T .
.
T T . . .
T T .
. .
4
1
2
2 1
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Some authors have proposed varying the position of the degree symbol to indicate whether a temperature or temperature interval is denoted; that is, 5 C refers to a temperature of five degrees Celsius, and 5C means an interval of five Celsius degrees. This idea, while an excellent one in principle, has not caught on, so you will have to get used to making the distinction yourself from the context in which the unit appears.
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4
T
Consider the interval from 20 F to 80 F.
Calculate the equivalent temperatures in C and the interval between them.
Calculate directly the interval in C between the temperatures.
From Equation 3.5-4,
( F) 32
( C) 1 8
so that
20 32
(20 F) C 6 7 C
1 8 80 32
(80 F) C 26 6 C
1 8 and
(26 6 ( 6 7)) C 33 3 C From Equation 3.5-5,
( F) 1 C (80 20) F 1 C
( C) 33 3 C
1 8 F 1 8 F
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For example, to find the number of Celsius degrees between 32 F and 212 F you can say that
(212 32) F 1 C
( C) 100 C
1.8 F
but to find the Celsuis temperature corresponding to 32 F you must use Equation 3.5-4;
you cannot say
Suppose you were given a glass tube with mercury in it but no scale markings, and you were given only a beaker of water, a freezer, and a bunsen burner with which to work.
How would you calibrate the thermometer to provide readings in C?
Which is warmer, a temperature of 1 C or 1 F?
Which reflects a greater change in temperature, an increase of 1 C or 1 F?
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density
specific ra ity
atomic wei ht
EXAMPLE 3.5-3 Temperature Con ersion and Dimensional Homo eneity
SOLUTION T
Example:
could Example: