FHSST Physics/Units/Temperature

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The Free High School Science Texts: A Textbook for High School Students Studying Physics
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Units
PGCE Comments - TO DO LIST - Introduction - Unit Systems - The Importance of Units - Choice of Units - How to Change Units - How Units Can Help You - Temperature - Scientific Notation, Significant Figures, and Rounding - Conclusion

Temperature[edit]

In everyday life, many people measure temperatures in Celsius. But in physics, we prefer to use the Kelvin scale which starts at absolute zero(−273.15 °C).

As we all know, Celsius temperatures can be negative. This might suggest that any number is a valid temperature. In fact, the temperature of a gas is a measure of the average kinetic energy of the particles that make up the gas. As we lower the temperature so the motion of the particles is reduced until a point is reached where all motion ceases. The temperature at which this occurs is called absolute zero. There is no physically possible temperature colder than this. In Celsius, absolute zero is at -273.15 °C. In Kelvin, the ordinary freezing point of water 0°C is therefore 273.15 °K

Physicists have defined a new temperature scale called the Kelvin scale. According to this scale absolute zero is at 0 K and negative temperatures are not allowed. The size of one unit kelvin is exactly the same as that of one unit degree Celsius. This means that a change in temperature of 1 kelvin is equal to a change in temperature of 1 degree Celsius—the scales just start in different places. Think of two ladders with steps that are the same size but the bottom most step on the Celsius ladder is labelled -273, while the first step on the Kelvin ladder is labelled 0. There are still 100 'steps' or degrees (Celsius or Kelvin) between the points where water freezes and boils when it is at at 1.0 atmosphere of pressure (water boils at lower temperatures if the air pressure is lowerO.


                         |----|   102 degrees Celsius    |----|  375 kelvin
                         |----|   101 degrees Celsius    |----|  374 kelvin
 water boils  --->       |----|   100 degrees Celsius    |----|  373 kelvin
                         |----|   99  degrees Celsius    |----|  372 kelvin
                         |----|   98  degrees Celsius    |----|  371 kelvin
                                             .
                                             .
                                             .
                         |----|   2   degrees Celsius    |----|  275 kelvin
                         |----|   1   degree Celsius     |----|  274 kelvin
 ice melts    --->       |----|   0   degrees Celsius    |----|  273 kelvin
                         |----|   -1  degree Celsius     |----|  272 kelvin
                         |----|   -2  degrees Celsius    |----|  271 kelvin
                                             .
                                             .
                                             .
                         |----|  -269 degrees Celsius    |----|  4 kelvin
                         |----|  -270 degrees Celsius    |----|  3 kelvin
                         |----|  -271 degrees Celsius    |----|  2 kelvin
                         |----|  -272 degrees Celsius    |----|  1 kelvin
 absolute zero --->      |----|  -273 degrees Celsius    |----|  0 kelvin
 

(NOTE TO SELF: Come up with a decent picture of two ladders with the labels --water boiling and freezing--in the same place but with different labelling on the steps!)

This makes the conversion from kelvin to degree Celsius and back very easy. To convert from degrees Celsius to kelvins add 273. To convert from kelvins to degrees Celsius subtract 273. Representing the Kelvin temperature by TK and the Celsius temperature by T°C,

\begin{matrix}T_K &=& T_{oC} + 273\end{matrix}
or
\begin{matrix}T_{oC} &=& T_K - 273\end{matrix}

Converting between kelvin and Celsius is additive -- so a difference in temperature of 1 degree Celsius is equal to a difference of 1 kelvin. The majority of conversions between units are multiplicative. For example, to convert from metres to millimetres we multiply by 1000. Therefore a change of 1 m is equal to a change of 1000 mm.

Although it seems as though there is not much reason for the scientific community to use the Kelvin scale over the Celsius scale, there is actually a very remarkable difference in using the Kelvin scale other than the reminding effect stated above. It happens that the idealised form of some materials varies proportionately according to the Kelvin scale, such that some required values can be simply found by multiplication and division. In such calculations, it is just a chore to use the Celsius scale.


Fahrenheit Scale[edit]

Fahrenheit is a temperature scale previously used in meteorology until about 1970, and which is still widely used in the USA. It was devised by a German physicist in 1724. He needed a scale that went below the freezing point of water, and used a mixture of ice, water, and ammonium chloride which freezes at a much lower temperature.

In this scale, the freezing point of water (0°C) is 32 degrees Fahrenheit (32°F) and the boiling point (100°C) is 212 °F, placing the boiling and freezing points of water exactly 180 degrees apart. A temperature interval of one degree Fahrenheit is an interval of 5⁄9 of a degree Celsius. The Fahrenheit and Celsius scales coincide at −40 degrees (i.e. −40 °F and −40 °C describe the same temperature).

To convert Celsius to Fahrenheit:

1) Take your number in Celsius and multiply by 9.

2) Divide the result of step 1 by 5.

3) Add 32 to the result of step 2.


Converting Fahrenheit to Celsius:

1) Take your number in Fahrenheit and subtract 32

2) Multiply the result of step 1 by 5.

3) Divide the result of step 2 by 9.

Rankine Scale[edit]

Absolute zero is −459.67 °F. The Rankine temperature scale was created to use degrees the same size as those of the Fahrenheit scale, such that a temperature difference of one degree Rankine (1 °R) is the same as a temperature difference of 1 °F, but with absolute zero being 0 °R.