The sense of touch provides some indication of the temperature of an object but is unreliable. For example, the metal shelf in the refrigerator feels colder than the food sitting on the shelf, even though they are in thermal equilibrium. The metal feels colder because the metal conducts the heat from your hand more efficiently.
Thermometers are instruments that define and measure the temperature of a system. The common thermometer consists of a volume of mercury that expands into a capillary tube when heated. When the thermometer is in thermal equilibrium with an object, the temperature can be read from the thermometer scale.
Three temperature scales are commonly used: Celsius, Fahrenheit, and Kelvin (also called absolute). Comparisons of the Celsius and Fahrenheit thermometers are shown in Figure 1.
Comparison of Celsius and Fahrenheit thermometers.
On the Celsius scale, the ice point is 0, and the steam point is 100. The interval between these temperatures is divided into 100 equal parts called degrees. As shown in Figure , on the Fahrenheit scale, the ice point is 32 degrees, and the steam point is 212 degrees. The interval between these temperatures is divided into 180 equal parts. The following equations relate temperature in Celsius (C) and Fahrenheit (F):
The Kelvin scale (K) has degrees of the same size as the Celsius scale, but the zero is shifted to the triple point of water. The triple point of water exists when water within a closed vessel is in equilibrium in all three states: ice, water, and vapor. This point is defined as 273.16 Kelvin and equals .01 degrees Celsius; therefore, to convert Celsius to Kelvin, simply add 273.15. Note that because the degrees are the same in the two scales, temperature differences are the same in either Celsius or Kelvin.
A mercury thermometer utilizes thermal expansion: the phenomenon that most substances increase in volume as their temperature increases. A rod that is heated will change in length (Δ L) according to Δ L = α L 0 Δ T, where L 0 is the original length and Δ T (delta T) change in temprature. The constant α (Greek letter alpha) is the average coefficient of linear expansion. This value is found in tables of coefficients for different materials and is measured in units of (degrees C) −1.
Not only does length change with a change in temperature, but area and volume change also. Thus, Δ A = γ A 0Δ T, where Δ A is the change in the original area A 0. The Greek letter gamma (γ) is the average coefficient of area expansion, which equals 2α. For change in volume, Δ V = β V 0, Δ T, where Δ V is the change in the original volume V 0. The Greek letter beta (β) is the average coefficient of volume expansion, which is equal to 3α.
Example 1: As an example of the application of these equations, consider heating a steel washer. What will be the area of the washer hole with original cross‐sectional area of 10 mm 2 if the steel has α = 1.1 × 10 −5 per °C and is heated from 20 degrees C to 70 degrees C?
Solution: The hole will expand the same as a piece of the material having the same dimensions. The equation for increase in area leads to the following:
Therefore, the new area of the hole will be 10.011 mm 2.
Water is an exception to the usual increase in volume with increasing temperature. Note in Figure 2 that the maximum density of water occurs at 4 degrees Celsius.
The density of water changes as the temperature changes.
This characteristic of water explains why a lake freezes at the surface. To see this, imagine that the air cools from 10 degrees Celsius to 5 degrees Celsius. The surface water in equilibrium with the air at these temperatures is denser than the slightly warmer water below it; therefore, the colder water sinks and warmer water from below comes to the surface. This occurs until the air temperature decreases to below 4 degrees when the surface water is less dense than the deeper water of about 4 degrees; then, the mixing ceases. As the temperature of the air continues to fall, the surface water freezes. The less dense ice remains on top of the water. Under these conditions, life near the bottom of the lake can continue to survive because only the water at or near the surface is frozen. Life on earth might have evolved quite differently if a pool of water froze from the bottom up.