Make the following conversions and include an equation for...

Make the following conversions and include an equation for each one:
(a) $32^{\circ} \mathrm{C}$ to ${ }^{\circ} \mathrm{F}$
(b) $-8.6^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$
(c) $273^{\circ} \mathrm{C}$ to $\mathrm{K}$
(d) $100 \mathrm{~K}$ to ${ }^{\circ} \mathrm{F}$

Key Concepts

Linear Conversion Equations

Conversions between temperature scales are typically performed using linear equations. These equations involve a scaling factor (slope) and an offset (intercept) to adjust for the differences in unit size and starting point between the scales.

Kelvin to Fahrenheit Conversion

The conversion from Kelvin to Fahrenheit involves two steps: first converting Kelvin to Celsius by subtracting 273.15, then converting Celsius to Fahrenheit using the linear relationship F = (C × 9/5) + 32. This combination addresses both the shift in baseline and the scaling factor between the temperature units.

Celsius to Kelvin Conversion

Converting Celsius to Kelvin is straightforward because the Kelvin scale is an absolute temperature scale that differs from Celsius by a constant offset. The conversion is performed using the equation K = C + 273.15.

Temperature Scales

Temperature scales such as Celsius, Fahrenheit, and Kelvin provide different ways of measuring thermal energy. Each scale has its own zero point and increment size, and understanding these differences is crucial for accurately converting measurements from one scale to another.

Celsius to Fahrenheit Conversion

The conversion from Celsius to Fahrenheit is achieved through the equation F = (C × 9/5) + 32. This formula reflects the ratio between the degrees in the Celsius and Fahrenheit scales and adjusts for the shift in the zero point between them.

Fahrenheit to Celsius Conversion

To convert temperatures from Fahrenheit to Celsius, the formula C = (F - 32) × 5/9 is used. This equation subtracts the Fahrenheit zero offset and scales the result to the Celsius degree size.

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