Thermal Physics - Lesson 1 - Heat and Temperature
Methods of Heat Transfer
• Introduction to Thermal Physics
• Temperature and Thermometers
• Thermometers as Speedometers
• What is Heat?
• Methods of Heat Transfer
• Rates of Heat Transfer
If you have been following along since the beginning of this lesson, then you have been developing a progressively sophisticated understanding of temperature and heat. You should be developing a model of matter as consisting of particles which vibrate (wiggle about a fixed position), translate (move from one location to another) and even rotate (revolve about an imaginary axis). These motions give the particles kinetic energy. Temperature is a measure of the average amount of kinetic energy possessed by the particles in a sample of matter. The more the particles vibrate, translate and rotate, the greater the temperature of the object. You have hopefully adopted an understanding of heat as a flow of energy from a higher temperature object to a lower temperature object. It is the temperature difference between the two neighboring objects that causes this heat transfer. The heat transfer continues until the two objects have reached thermal equilibrium and are at the same temperature. The discussion of heat transfer has been structured around some everyday examples such as the cooling of a hot mug of coffee and the warming of a cold can of pop. Finally, we have explored a thought experiment in which a metal can containing hot water is placed within a Styrofoam cup containing cold water. Heat is transferred from the hot water to the cold water until both samples have the same temperature.
Now we should probe some of the following questions:
• What is happening at the particle level when energy is being transferred between two objects?
• Why is thermal equilibrium always established when two objects transfer heat?
• How does heat transfer work within the bulk of an object?
• Is there more than one method of heat transfer? If so, then how are they similar and different than one another?
Conduction - A Particle View
Let's begin our discussion by returning to our thought experiment in which a metal can containing hot water was placed within a Styrofoam cup containing cold water. Heat is transferred from the hot water to the cold water until both samples have the same temperature. In this instance, the transfer of heat from the hot water through the metal can to the cold water is sometimes referred to as conduction. Conductive heat flow involves the transfer of heat from one location to another in the absence of any material flow. There is nothing physical or material moving from the hot water to the cold water. Only energy is transferred from the hot water to the cold water. Other than the loss of energy, there is nothing else escaping from the hot water. And other than the gain of energy, there is nothing else entering the cold water. How does this happen? What is the mechanism that makes conductive heat flow possible?
A question like this is a particle-level question. To understand the answer, we have to think about matter as consisting of tiny particles atoms, molecules and ions. These particles are in constant motion; this gives them kinetic energy. As mentioned previously in this lesson, these particles move throughout the space of a container, colliding with each other and with the walls of their container. This is known as translational kinetic energy and is the main form of kinetic energy for gases and liquids. But these particles can also vibrate about a fixed position. This gives the particles vibrational kinetic energy and is the main form of kinetic energy for solids. To put it more simply, matter consists of little wigglers and little bangers. The wigglers are those particles vibrating about a fixed position. They possess vibrational kinetic energy. The bangers are those particles that move through the container with translational kinetic energy and collide with the container walls.
The container walls represent the perimeters of a sample of matter. Just as the perimeter of your property (as in real estate property) is the furthest extension of the property, so the perimeter of an object is the furthest extension of the particles within a sample of matter. At the perimeter, the little bangers are colliding with particles of another substance - the particles of the container or even the surrounding air. Even the wigglers that are fixed in a position along the perimeter are doing some banging. Being at the perimeter, their wiggling results in collisions with the particles that are next to them; these are the particles of the container or of the surrounding air.
At this perimeter or boundary, the collisions of the little bangers and wigglers are elastic collisions in which the total amount of kinetic energy of all colliding particles is conserved. The net effect of these elastic collisions is that there is a transfer of kinetic energy across the boundary to the particles on the opposite side. The more energetic particles will lose a little kinetic energy and the less energetic particles will gain a little kinetic energy. Temperature is a measure of the average amount of kinetic energy possessed by the particles in a sample of matter. So on average, there are more particles in the higher temperature object with greater kinetic energy than there are in the lower temperature object. So when we average all the collisions together and apply the principles associated with elastic collisions to the particles within a sample of matter, it is logical to conclude that the higher temperature object will lose some kinetic energy and the lower temperature object will gain some kinetic energy. The collisions of our little bangers and wigglers will continue to transfer energy until the temperatures of the two objects are identical. When this state of thermal equilibrium has been reached, the average kinetic energy of both objects' particles is equal. At thermal equilibrium, there are an equal number of collisions resulting in an energy gain as there are collisions resulting in an energy loss. On average, there is no net energy transfer resulting from the collisions of particles at the perimeter.
At the macroscopic level, heat is the transfer of energy from the high temperature object to the low temperature object. At the particle level, heat flow can be explained in terms of the net effect of the collisions of a whole bunch of little bangers. Warming and cooling is the macroscopic result of this particle-level phenomenon. Now let's apply this particle view to the scenario of the metal can with the hot water positioned inside of a Styrofoam cup containing cold water. On average, the particles with the greatest kinetic energy are the particles of the hot water. Being a fluid, those particles move about with translational kinetic energy and bang upon the particles of the metal can. As the hot water particles bang upon the particles of the metal can, they transfer energy to the metal can. This warms the metal can up. Most metals are good thermal conductors so they warm up quite quickly throughout the bulk of the can. The can assumes nearly the same temperature as the hot water. Being a solid, the metal can consists of little wigglers. The wigglers at the outer perimeter of the metal can bang upon particles in the cold water. The collisions between the particles of the metal can and the particles of the cold water result in the transfer of energy to the cold water. This slowly warms the cold water up. The interaction between the particles of the hot water, the metal can and the cold water results in a transfer of energy outward from the hot water to the cold water. The average kinetic energy of the hot water particles gradually decreases; the average kinetic energy of the cold-water particles gradually increases; and eventually, thermal equilibrium would be reached at the point that the particles of the hot water and the cold water have the same average kinetic energy. At the macroscopic level, one would observe a decrease in temperature of the hot water and an increase in temperature of the cold water.
The mechanism in which heat is transferred from one object to another object through particle collisions is known as conduction. In conduction, there is no net transfer of physical stuff between the objects. Nothing material moves across the boundary. The changes in temperature are wholly explained as the result of the gains and losses of kinetic energy during collisions.
Conduction Through The Bulk of an Object
We have discussed how heat transfers from one object to another through conduction. But how does it transfer through the bulk of an object? For instance, suppose we pull a ceramic coffee mug out of the cupboard and place it on the countertop. The mug is at room temperature - maybe at 26°C. Then suppose we fill the ceramic coffee mug with hot coffee at a temperature of 80°C. The mug quickly warms up. Energy first flows into the particles at the boundary between the hot coffee and the ceramic mug. But then it flows through the bulk of the ceramic to all parts of the ceramic mug. How does heat conduction occur in the ceramic itself?
The mechanism of heat transfer through the bulk of the ceramic mug is described in a similar manner as it before. The ceramic mug consists of a collection of orderly arranged wigglers. These are particles that wiggle about a fixed position. As the ceramic particles at the boundary between the hot coffee and the mug warm up, they attain a kinetic energy that is much higher than their neighbors. As they wiggle more vigorously, they bang into their neighbors and increase their vibrational kinetic energy. These particles in turn begin to wiggle more vigorously and their collisions with their neighbors increase their vibrational kinetic energy. The process of energy transfer by means of the little bangers continues from the particles at