Temperature Conversions (Units: A Unit Conversion Program and Scientific Calculator)

### 6.1 Temperature Conversions ¶

Conversions between temperatures are different from linear conversions between temperature increments—see the example below. The absolute temperature conversions are handled by units starting with ‘`temp`’, and you must use functional notation. The temperature-increment conversions are done using units starting with ‘`deg`’ and they do not require functional notation.

    You have: tempF(45)
    You want: tempC
            7.2222222

    You have: 45 degF
    You want: degC
            * 25
            / 0.04

Think of ‘`tempF(x)`’ not as a function but as a notation that indicates that x should have units of ‘`tempF`’ attached to it. See Defining Nonlinear Units. The first conversion shows that if it’s 45 degrees Fahrenheit outside, it’s 7.2 degrees Celsius. The second conversion indicates that a change of 45 degrees Fahrenheit corresponds to a change of 25 degrees Celsius. The conversion from ‘`tempF(x)`’ is to absolute temperature, so that

    You have: tempF(45)
    You want: degR
            * 504.67
            / 0.0019814929

gives the same result as

    You have: tempF(45)
    You want: tempR
            * 504.67
            / 0.0019814929

But if you convert ‘`tempF(x)`’ to ‘`degC`’, the output is probably not what you expect:

    You have: tempF(45)
    You want: degC
            * 280.37222
            / 0.0035666871

The result is the temperature in K, because ‘`degC`’ is defined as ‘`K`’, the kelvin. For consistent results, use the ‘`tempX`’ units when converting to a temperature rather than converting a temperature increment.

The ‘`tempC()`’ and ‘`tempF()`’ definitions are limited to positive absolute temperatures, and giving a value that would result in a negative absolute temperature generates an error message:

    You have: tempC(-275)
                        ^
    Argument of function outside domain