8.2: Heat Transfer

 Learning Objectives

• To relate heat transfer to temperature change.
• Memorize temperature equations for Celsius, Fahrenheit and Kelvin conversions.
• Understand how body temperature can vary.

The concept of temperature may seem familiar to you, but many people confuse temperature with heat. Temperature is a measure of how hot or cold an object is relative to another object (its thermal energy content), whereas heat is the flow of thermal energy between objects with different temperatures. When we touch a hot object, energy flows from the hot object into our fingers, and we perceive that incoming energy as the object being “hot.” Conversely, when we hold an ice cube in our palms, energy flows from our hand into the ice cube, and we perceive that loss of energy as “cold.” In both cases, the temperature of the object is different from the temperature of our hand, so we can conclude that differences in temperatures are the ultimate cause of heat transfer.

Temperature Scales

You will recall from previous reading that temperature is a measure of the average amount of energy of motion, or kinetic energy, a system contains. Temperatures are expressed using scales that use units called degrees. There are three scales used for reporting temperatures. Figure \(\PageIndex{1}\) compares the three temperature scales: Fahrenheit (expressed as °F), Celsius (°C), and Kelvin (K). Thermometers measure temperature by using materials that expand or contract when heated or cooled. Mercury or alcohol thermometers, for example, have a reservoir of liquid that expands when heated and contracts when cooled, so the liquid column lengthens or shortens as the temperature of the liquid changes.

Heat transfer

Heat is a familiar manifestation of energy. When we touch a hot object, energy flows from the hot object into our fingers, and we perceive that incoming energy as the object being “hot.” Conversely, when we hold an ice cube in our palms, energy flows from our hand into the ice cube, and we perceive that loss of energy as “cold.” In both cases, the temperature of the object is different from the temperature of our hand, so we can conclude that differences in temperatures are the ultimate cause of heat transfer.

Suppose we consider the transfer of heat from the opposite perspective—namely, what happens to a system that gains or loses heat? Generally, the system’s temperature changes. (We will address a few exceptions later.) The greater the original temperature difference, the greater the transfer of heat, and the greater the ultimate temperature change. The relationship between the amount of heat transferred and the temperature change can be written as

\[\text{heat} \propto ΔT \label{Eq1} \]

where ∝ means “is proportional to” and ΔT is the change in temperature of the system. Any change in a variable is always defined as “the final value minus the initial value” of the variable, so ΔT is T_final − T_initial. In addition, the greater the mass of an object, the more heat is needed to change its temperature. We can include a variable representing mass (m) to the proportionality as follows:

\[\text{heat} \propto mΔT \label{Eq2} \]

To change this proportionality into an equality, we include a proportionality constant. The proportionality constant is called the specific heat and is commonly symbolized by \(c\):

\[\text{heat} = mcΔT \label{Eq3} \]

Every substance has a characteristic specific heat, which is reported in units of cal/g•°C or cal/g•K, depending on the units used to express ΔT. The specific heat of a substance is the amount of energy that must be transferred to or from 1 g of that substance to change its temperature by 1°. Table \(\PageIndex{1}\) lists the specific heats for various materials. (For the specific heats of many foods, refer to TheEngineeringToolbox.com.)

Table \(\PageIndex{1}\): Specific Heats of Selected Substances

Substance	c (cal/g•°C)
aluminum (Al)	0.215
aluminum oxide (Al2O3)	0.305
bananas	0.8
butter	0.65
beef, loin	0.66
carrots	0.91
eggs	0.76
ice [H2O(s)]	0.492
flour	0.38
lemons	0.91
milk, whole, cows	0.90
pineapple, fresh	0.88
sodium chloride (NaCl)	0.207
steam [H2O(g)]	0.488
water [H2O(ℓ)]	1.00

The proportionality constant c is sometimes referred to as the specific heat capacity or (incorrectly) the heat capacity.

The direction of heat flow is not shown in heat = mcΔT. If energy goes into an object, the total energy of the object increases, and the values of heat ΔT are positive. If energy is coming out of an object, the total energy of the object decreases, and the values of heat and ΔT are negative.

For Example (you will not be asked to complete calculations like these). \(\PageIndex{3}\)

What quantity of heat is transferred when a 150.0 g block of iron metal is heated from 25.0°C to 73.3°C? What is the direction of heat flow?

Solution

We can use Equation \ref{Eq3} to determine the amount of heat, but first we need to determine ΔT. Because the final temperature of the iron is 73.3°C and the initial temperature is 25.0°C, ΔT is as follows:

\[\begin{align*} ΔT = T_{final} − T_{initial} \\[4pt] &= 73.3^oC − 25.0^oC \\[4pt] &= 48.3^oC \end{align*} \nonumber \]

The mass is given as 150.0 g, and Table \(\PageIndex{1}\) gives the specific heat of iron as 0.108 cal/g•°C. Substitute the known values into Equation \ref{Eq3} and solve for amount of heat:

\[\mathrm{heat=(150.0\: g)\left(0.108\: \dfrac{cal} {g\cdot {^\circ C}}\right)(48.3^\circ C) = 782\: cal} \nonumber \]

Note how the gram and °C units cancel algebraically, leaving only the calorie unit, which is a unit of heat. Because the temperature of the iron increases, energy (as heat) must be flowing into the metal.

 

Exercise \(\PageIndex{4}\)

A 10.7 g crystal of table salt (sodium chloride, NaCl) had an initial temperature of 37.0°C. What is the final temperature of the crystal if 147 cal of heat were supplied to it?

Answer

103.4°C

Notice that water has a very high specific heat compared to most other substances. Water is commonly used as a coolant for machinery because it is able to absorb large quantities of heat (see table above). Coastal climates are much more moderate than inland climates because of the presence of the ocean. Water in lakes or oceans absorbs heat from the air on hot days and releases it back into the air on cool days.

Figure \(\PageIndex{2}\): Pots being heated with a wood-burning fire in South India. The heat from the combustion of the wood is transfered to the metal of the pot, and then to the contents of the pot.
Image credit: By Vasanth Bantakal - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/inde...curid=87224724

Summary

• Heat transfer is related to temperature change.
• The specific heat of a substance is the amount of energy required to raise the temperature of 1 gram of the substance by \(1^\text{o} \text{C}\).