(a) The temperature on a warm summer day is 87^∘ F . What is the temperature in ^∘ C ? (b) Many

step 1 So now we'll work on problem 34 from chapter 1. This question is related, has several parts, all

(a) The temperature on a warm summer day is 87^∘ F . What is...

(a) The temperature on a warm summer day is $87^{\circ} \mathrm{F}$ . What is the temperature in $^{\circ} \mathrm{C} ?$ (b) Many scientific data are reported at $25^{\circ} \mathrm{C}$ . What is this temperature in kelvins and in degrees Fahrenheit? (c) Suppose that a recipe calls for an oven temperature of $400^{\circ} \mathrm{F}$ . Convert this temperature to degrees Celsius and to kelvins. (d) Liquid nitrogen boils at 77 $\mathrm{K}$ . Convert this temperature to degrees Fahrenheit and to degrees Celsius.

Key Concepts

Temperature Offsets and Absolute Zero

The concept of offsets is critical in temperature conversions because not all temperature scales start from zero at the same physical condition. Both the Fahrenheit and Celsius scales have arbitrary zero points based on the properties of water, whereas Kelvin is rooted in absolute thermodynamic temperature. Understanding the offset—such as the 32-degree and 273.15-degree adjustments—is essential to correctly convert temperature values between the various scales.

Temperature Scales

Temperature measurement is carried out using different scales, most notably Fahrenheit (°F), Celsius (°C), and Kelvin (K). Each scale has its own reference points: the Celsius scale defines 0 °C as the freezing point of water and 100 °C as the boiling point at standard atmospheric pressure, while the Fahrenheit scale sets water’s freezing point at 32 °F and boiling point at 212 °F. The Kelvin scale, on the other hand, is an absolute scale starting at absolute zero, the point at which all thermal motion ceases, with water freezing at 273.15 K under standard conditions.

Conversion Formulas

Conversions between temperature scales are based on linear equations that account for both scaling differences and offset adjustments. For example, converting Celsius to Fahrenheit involves multiplication by 9/5 and then adding 32, while converting Fahrenheit back to Celsius requires subtraction of 32 followed by multiplication by 5/9. Similarly, the Kelvin and Celsius scales are related by an offset of 273.15, where Kelvin equals Celsius plus 273.15, which allows straightforward conversion between these two scales.

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