## TemperatureEdit

We need to make a special mention of the units used to describe temperature. The unit of temperature listed in Table 1.1 is not the everyday unit we see and use.

Normally the Celsius scale is used to describe temperature. 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.

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 between the points where water freezes and boils on either ladder.

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

(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 kelvins to degrees 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 *T*_{K} and the Celsius temperature by *T*_{oC},

It is because this conversion is additive that 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.

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