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

Make the following conversions and include an equation for each one:
(a) $162^{\circ} \mathrm{F}$ to ${ }^{\circ} \mathrm{C}$
(b) $0.0^{\circ} \mathrm{F}$ to K
(c) $-18^{\circ} \mathrm{C}$ to ${ }^{\circ} \mathrm{F}$
(d) 212 K to ${ }^{\circ} \mathrm{C}$

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Key Concepts

Temperature Scales

Temperature scales are systems for measuring temperature. The most common scales include Fahrenheit, Celsius, and Kelvin. Each scale defines temperature differently; for example, the Celsius scale is based on the freezing and boiling points of water, Fahrenheit uses a different interval between these points, and Kelvin is an absolute temperature scale starting at absolute zero, which is useful for scientific calculations.

Conversion Equations

Conversion equations are the mathematical formulas used to translate a temperature value from one scale to another. These equations typically consist of a multiplicative factor and an additive offset. For instance, converting between Fahrenheit and Celsius involves subtracting an offset and then multiplying by a conversion factor, which aligns the different interval widths and starting points of the scales.

Offset and Scaling Factors

When converting between temperature scales, both an offset and a scaling factor need to be applied to account for differences in where the zero point is set and the size of the temperature unit. The offset adjusts for the difference in baseline (such as the freezing point of water in Celsius versus Fahrenheit), while the scaling factor compensates for the differing increments between temperature marks on each scale.

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