# 13.1: Temperature

Difficulty Level: At Grade Created by: CK-12

## Objectives

The student will:

• Explain what is meant by temperature.
• Use the centigrade (Celsius) and Kelvin temperature scales.

## Vocabulary

• temperature: measurement of the average kinetic energy of the molecules in an object or system. Temperature can be measured with a thermometer or a calorimeter.

### Introduction

Objects that appear to be motionless with the human eye still have motion inside them. Matter is typically found in three states: solids, liquids, and gases. Solids have their molecules rigidly bound together by electrical forces, but the molecules can still vibrate back and forth in place. Liquids have molecules that touch and attract each other, but can move freely around each other. Gases have almost no electrical attraction between their molecules, and can move freely in any direction.

Temperature is a measure of the motion of the molecules of a substance. It is traditionally measured with a thermometer, which uses a liquid that can readily expand and contract in a tube. As the liquid gets hotter, it expands and shows a higher number on the tube. There are two closely related metric units of temperature– degrees Celsius, C\begin{align*}^\circ \text{C}\end{align*}, and Kelvin, K\begin{align*}\text{K}\end{align*}, as well as the common non-metric unit, degrees Fahrenheit, F\begin{align*}^\circ \text{F}\end{align*}.

### The Fahrenheit Scale

The first modern thermometer was invented by Daniel Fahrenheit (1686-1736), shown in the Figure below. The Fahrenheit scale is common in the United States but rarely used elsewhere. The scale was originally based on the range between zero at the temperature of brine (an equal mix of ice, water, and ammonium chloride) and 100 at average human body temperature.

Daniel Fahrenheit

The average is closer to 66.6 degrees above freezing (98.6 degrees). Since the freezing and boiling points of water make for good references, they were kept, and the average human body temperature was readjusted.

### The Celsius Scale

The two metric scales are based on the work of Swedish astronomer Anders Celsius, shown in the Figure below. His scale also was defined from zero to 100, but the scale was based on the freezing point and boiling point of water. Zero degrees Celsius, 0C\begin{align*}0^\circ \text{C}\end{align*}, is the temperature at which water freezes under standard conditions, and one hundred degrees Celsius, 100C\begin{align*}100^\circ \text{C}\end{align*}, is the temperature at which water boils under standard conditions.

Anders Celsius

### The Kelvin Scale

The other metric scale was invented later, after it was determined that temperature is based on motion. William Thomson, titled Lord Kelvin (1824 - 1907), Figure below, was an Irish physicist and engineer who devised a temperature scale that had an absolute zero. Although he did not fully understand the nature of heat, his calculations predicted there was a minimum temperature where the object had absolutely no heat.

Lord Kelvin

The lowest temperature (0 °K) on the Kelvin scale is equal to “absolute zero” or about -273 °C on the Celsius scale. The relationship between the two scales is a simple one: If you’re given a temperature Tc\begin{align*}T_c\end{align*} measured in the Celsius scale of xC\begin{align*}x^\circ C\end{align*} and wish to find the corresponding temperature TK\begin{align*}T_{K}\end{align*} in the Kelvin scale, then:TK=TC(1KC)+273K\begin{align*}T_K=T_C \left(1 \frac{K}{C}\right)+273 K\end{align*} or more simply TK=TC+273\begin{align*}\rightarrow T_K=T_C+273\end{align*}, where the answer is in units of Kelvin.

1. What is a temperature of 20 °C in Kelvin?

Answer: TK=TC+273 TK=20+273=293K\begin{align*}T_K=T_C+273 \ T_K=20+273=293 K\end{align*}

2. What is the temperature of -300 °C in Kelvin?

Answer: TK=TC+273TK=300+273=27K\begin{align*}T_K=T_C+273 \rightarrow T_K=-300+273=-27 K\end{align*}

This answer is impossible. 0 K is the lowest possible temperature. There can be no temperature lower than 273C\begin{align*}-273^\circ C\end{align*}.

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Date Created:
Mar 11, 2013