The relationships between the three common temperature scales is shown inFigure 13.6. Temperatures on these scales can be converted using the
equations inTable 13.1.Table 13.1Temperature Conversions
To convert from... Use this equation... Also written as...Celsius to Fahrenheit T(ºF)=
9
5
T(ºC)+ 32 TºF=^9
5
TºC+ 32
Fahrenheit to Celsius T(ºC)=
5
9
⎛⎝T(ºF)− 32
⎞⎠ TºC=^5
9
⎛⎝TºF− 32
⎞
⎠Celsius to Kelvin T(K)=T(ºC)+ 273.15 TK=TºC+ 273.^15
Kelvin to Celsius T(ºC)=T(K)− 273.15 TºC=TK− 273.15
Fahrenheit to Kelvin T(K)=
5
9
⎛⎝T(ºF)− 32⎞⎠+ 273.15 T
K=
5
9
⎛⎝TºF− 32
⎞⎠+ 273.15
Kelvin to Fahrenheit T(ºF) =
9
5
⎛⎝T(K)− 273.15⎞⎠+ 32 T
ºF=
9
5
⎛⎝TK− 273.15
⎞⎠+ 32
Notice that the conversions between Fahrenheit and Kelvin look quite complicated. In fact, they are simple combinations of the conversions between
Fahrenheit and Celsius, and the conversions between Celsius and Kelvin.Example 13.1 Converting between Temperature Scales: Room Temperature
“Room temperature” is generally defined to be25ºC. (a) What is room temperature inºF? (b) What is it in K?
Strategy
To answer these questions, all we need to do is choose the correct conversion equations and plug in the known values.
Solution for (a)1. Choose the right equation. To convert fromºCtoºF, use the equation
T (13.1)
ºF=
9
5
TºC+ 32.
- Plug the known value into the equation and solve:
(13.2)
TºF=^9
5
25ºC + 32 = 77ºF.
Solution for (b)1. Choose the right equation. To convert fromºCto K, use the equation
TK=TºC+ 273. 15. (13.3)
- Plug the known value into the equation and solve:
TK= 25ºC + 273.15 = 298 K. (13.4)
Example 13.2 Converting between Temperature Scales: the Reaumur Scale
The Reaumur scale is a temperature scale that was used widely in Europe in the 18th and 19th centuries. On the Reaumur temperature scale,the freezing point of water is0ºRand the boiling temperature is80ºR. If “room temperature” is25ºCon the Celsius scale, what is it on the
Reaumur scale?
Strategy
To answer this question, we must compare the Reaumur scale to the Celsius scale. The difference between the freezing point and boiling pointof water on the Reaumur scale is80ºR. On the Celsius scale it is100ºC. Therefore100ºC = 80ºR. Both scales start at0ºfor freezing, so
we can derive a simple formula to convert between temperatures on the two scales.
Solution- Derive a formula to convert from one scale to the other:
(13.5)
TºR=0.8ºR
ºC
×TºC.
- Plug the known value into the equation and solve:
T (13.6)
ºR=
0.8ºR
ºC
× 25ºC = 20ºR.
434 CHAPTER 13 | TEMPERATURE, KINETIC THEORY, AND THE GAS LAWS
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