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Chapter 16: Problem 3

Compare the relative sizes of the kelvin, the degree Celsius, the degree Fahrenheit, and the degree Rankine.

Short Answer

Expert verified
Based on the conversion criteria, a change of one degree is smallest in Fahrenheit and largest in Rankine. Therefore, the relative sizes of the temperature scales are: 1掳F < 1掳C = 1 K < 1掳R.

Step by step solution

01

Understand the Temperature Scales

There are four common temperature scales: Kelvin, Celsius, Fahrenheit, and Rankine. Kelvin scale is the unit of temperature in the International System of Units (SI), Celsius is commonly used in everyday temperature readings, Rankine scale is used in engineering systems where heat computations are done, and Fahrenheit is used in the United States to measure temperatures. It's important to know that the Kelvin and Rankine scales start at absolute zero (0 K and 0 掳R are absolute zero), but the Celsius and Fahrenheit scales do not (0 掳C is the freezing point of water, and 32 掳F is also the freezing point of water).
02

Conversion Criteria

To compare the relative sizes of these units, we need to find a common basis. For simplicity, let's use a one-degree change in each. Celsius and Kelvin have the same magnitude, so 1 degree of change in Celsius is equivalent to 1 K. For Fahrenheit, 1 degree of change is equivalent to a difference of 5/9掳C or 5/9 K. For Rankine, 1 degree of change is the same as 5/9 K or 5/9掳C.
03

Rank the Scales

We can now rank the scales in terms of their relative sizes: 1掳F < 1掳C = 1 K < 1掳R. This tells us that a temperature change of 1 degree Fahrenheit is the smallest change among the four scales, and a change of 1 degree Rankine is the largest change.

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Most popular questions from this chapter

You arrive for a party on a night when it's \(8^{\circ} \mathrm{C}\) outside. Your hosts meet you at the door and say the party may need to be cancelled, because the heating system has failed and they don't want to discomfort their guests. You say, "Not so fast!" A total of 36 people are expected, the average power output of a human body is \(100 \mathrm{W},\) and the house loses energy at the rate \(320 \mathrm{W} / \mathrm{C} .\) Will the house remain comfortable?

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