Heat Transfer and Thermodynamics

 

Resources: Fordham Preparatory School; Encyclopedia.com; chemforkids; com; University of Florida, Department of Chemistry; USA Today; John Hopkins University; NTNU Virtual Physics Laboratory; UC Berkeley; MillsAps College; Physicsclassroom.com; Exploratorium

 

11.1 Heat Transfer and Thermodynamics

a. Know the principle of conservation of energy and apply it to energy transfers
b. Discuss how the transfer of energy as heat is related to changes in temperature
c. Diagram direction of heat flow in a system
d. Describe the methods of heat transfer by conduction, convection, and radiation and provide examples for all
e. Explain how chemical potential energy in fuel is transformed to heat
f. Design and explain experiments to induce a physical change such as freezing, melting, or boiling
g. Distinguish between physical and chemical changes and provide examples of each

Know the principle of conservation of energy and apply it to energy transfers

Principle of Conservation of Energy - Click on each of the four areas of Conservation of Energy to learn more

Heat Transfer Calculations

 

Diagram direction of heat flow in a system- energy transfers

First Law of Thermodynamics- enthalpy, system work (using calculus)- follow

Heat and work example

Second Law of Thermodynamics- examples - "It is impossible for heat to flow spontaneously from a colder body to a hotter body."

Heat Engine Cycle- examples

The Kinetic Theory of Gases

Conceptual Introduction to the Concepts of Gases - Activity

A quantitative and model view: Once the window appears when clicking on the link above, set the number of particles in the chamber to 100, the pressure outside of the cylinder to 50 and the velocity of the molecules to 100. Follow the directions below. Each time you put a new number into a box, PRESS RETURN/ENTER to set the value.

  • Record the volume INSIDE the cylinder (V: to the left of the screen). Set up a table with Pressure INSIDE the cylinder as the dependent variable (y-axis) and number of particles as the independent variable. Record the pressure reading, then double the number of particles (100), double them again (400) and double them once more (800). Each time record what happened to the Pressure. GRAPH THIS RELATIONSHIP IF YOU CAN'T SEE THE RELATIONSHIP FROM THE DATA. (GRAPH 1)
  • Set up a table with the volume INSIDE the cylinder as the dependent variable and the pressure OUTSIDE the cylinder as the independent variable. Keeping the number of particles at 800, now vary the Pressure OUTSIDE of the cylinder. Double it to 100, then double it again to 200 and finally to 400. Each time record the volume INSIDE the cylinder ONCE THE VALUE STABILIZES. If it doesn't record 5 values and average them. GRAPH THIS RELATIONSHIP IF YOU CAN'T SEE THE RELATIONSHIP FROM THE DATA. (GRAPH 2)
  • Set up a table with volume INSIDE the cylinder as the independent variable and the velocity as the dependent variable. Keeping the number of particles of gas and the outside pressure constant, begin to increase the velocity of the molecules. Record the volume inside the cylinder. Double the velocity to 200 and then double it again to 400. Each time record the INSIDE volume of the cylinder. GRAPH THIS RELATIONSHIP. GRAPH THE RELATIONSHIP IF YOU CAN'T SEE THE RELATIONSHIP FROM THE DATA. (GRAPH 3)
  • Answer the questions below.
    • What kind of relationship is there between the number of particles of gas inside the cylinder and the volume inside the cylinder? Explain why.
    • What kind of relationship is there between increased pressure OUTSIDE the cylinder and the volume inside the cylinder? Explain why.
    • What kind of relationship is there between increased velocity of the molecules of gas inside the cylinder and the volume inside the cylinder? Explain why. (Hint: use the equation for kinetic energy to help you)
    • A balloon is a good way to see if you understand the current concept. If you were to fly up to the stratosphere (like superman) where the NUMBER OF MOLECULES OUTSIDE THE BALLOON ARE MUCH LESS THAN THE number of MOLECULES INSIDE THE BALLOON... WHAT WOULD HAPPEN TO THE SIZE OF THE BALLOON IN THE STRATOSPHERE COMPARED TO ITS SIZE ON THE GROUND?

Pressure and Number of Molecules- Daltons Law

Temperature and volume- Charles Law

Pressure and Volume- Boyle's Law

 

 

The Ideal Gas Law From notes by Dr. David Taylor, Northwestern University

The Ideal Gas Law is:

PV = NkBT,   where

P = the pressure of the gas
V = the volume of the container the gas occupies
N = the number of molecules of gas in the container
kB = Boltzmann's constant
T = the temperature of the gas in K°

This equation has four variables in it (P, V, N, T) and that makes it hard to grasp. Frequently though, we can constrain two of the variables and then we only have to worry about a two-variable equation.

First, we can talk about a particular sample of gas inside a container. That fixes N, and we don't have to deal with it any further. We can just set NkB = constant, and for our purposes it doesn't matter what the constant is.

Let us consider the rest of the variables, (P, V, T), two at a time.

1) T = constant

If we fix the temperature, we are just left with PV = constant for the gas law. So, in this situation, if the volume is doubled, the pressure must go down by one-half. And vice-versa. The simplest illustration of this would be a cylinder with a plunger on one end: if you push the plunger in so that the volume of the cylinder is halved and the temperature remains constant, then the pressure will double.

However, it is important to realize that constant-temperature processes must be pretty slow ones (in other words, you must move the plunger on the gas cylinder very slowly) because there must be enough time for heat to flow between the inside and outside of the cylinder to keep everything at a constant temperature.

Suppose you don't do that. Suppose you just slam in the plunger very quickly. Well, you are exerting a force through a distance (as you push the cylinder in, the pressure inside resists, thus you are using force), and as we remember, E = Fd. So, energy is being expended as you force the plunger inwards. Where does that energy go? If you slam the plunger in quickly, it doesn't have time to leave the cylinder, so there is only one place for it to go: into the gas. In other words, the gas will heat up.

You can imagine the situation microscopically by visualizing the gas atoms inside the cylinder, bouncing around like ping-pong balls. Suppose one of the walls starts moving inwards. What happens to the atoms as they bounce against the wall moving towards them? Well, what happens to a baseball when it meets a bat moving towards it? The atoms bounce off the wall with a higher velocity than they had when they hit it. In other words, their temperature rises. In order for a cylinder with a plunger being pushed into it to remain at constant temperature, the plunger must be moved in so slowly that the heated gas atoms inside the cylinder have time to lose that heat to the outside world.

Note -- the diesel engine, unlike a gasoline engine, uses no spark plug. How does it ignite the fuel? It does it by simply operating at a very high pressure. When diesel fuel and air are sprayed inside the cylinder in a diesel engine, the cylinder is compressed so highly (and so fast) that the temperature of the fuel-air mixture rises enough to ignite itself. No other heat input is necessary.

The opposite of the above effect is provided by putting compressed gas into the cylinder, then letting go of the plunger. The high-pressure gas will drive the plunger out -- and the energy to accelerate the plunger has to come from somewhere. It can only come from the gas inside the cylinder, so the gas temperature will fall. (It is left as an exercise to the reader to imagine ping-pong balls hitting a wall and moving it outwards, and thereby losing velocity.) The expansion can only occur at constant temperature if the expansion is very slow, so that the gas has time to absorb heat from the outside world.

2) V = constant

In this case, we can write P(const) = (const)T for the Ideal Gas Law, or just P = (const)T

In this case, the pressure will rise or fall directly with the temperature. Double the temperature, double the pressure. Constant volume is easy to achieve: you just need a gas inside a sealed container of some sort. The only caveat to be kept in mind here is that the temperature must be measured in degrees Kelvin. "Doubling the temperature" means that you go from 200 K° to 400 K°, not 50 F° to 100 F°.

Tech note -- Ever wonder why manufacturers warn you not to burn empty spray cans in a fire, lest they explode? You may have wondered (as I did, when I was a little kid), what exactly is it that is going to explode, if the can is empty? Well, in fact, the can wouldn't explode -- if it were truly "empty". But, it isn't empty. It has air inside, and if you heat that air enough, it might reach a high enough pressure to rupture the can, i.e., explode.

Microscopically, the V= constant case is easy to visualize. You have atoms bouncing around. You heat them up (or cool them down), i.e., you change their velocity. They then bang against the walls more (or less) energetically, which is exactly what we call pressure.

3) P = constant

This case gives us V = (const)T. Doubling the absolute temperature of a gas also doubles its volume, if the pressure is constant, and vice versa.

This case can sometimes be a bit tricky to visualize. A constant pressure can only be maintained if there is some force (usually external to the body of gas in question) maintaining a constant force on the gas. In class, I have used a demonstration device which consists of a cylinder filled with tiny blue pellets to simulate a gas. An agitator at the bottom whips up the pellets into a little hailstorm, thereby simulating the motion of gas atoms. A movable plunger setting on top of the cylinder has, of course, a constant weight and a constant area, so it represents a constant pressure. (Since P = force / area). Temperature is a measure of the average energy of atoms, and by whipping the pellets at different speeds I showed that the volume of the cylinder expanded as the speed of the pellets (i.e., their "temperature") was increased, and vice-versa.

Microscopically, we are just saying that gas atoms move faster as they gain heat (increase temperature). So, they pound the walls harder and create higher pressure. If the wall is free to move, than it will do so, because unbalanced pressures on opposites sides of a wall mean unbalanced forces, and thus the wall must move unless it is clamped into place.

But why did plunger in my demonstration eventually stop? If the atoms (blue balls) are at the same temperature, then they are still moving at the same speed. Why don't they just push out the plunger forever?

To answer this, we must realize that the pressure on the wall is affected not only by how fast the balls (atoms) are hitting it, but also how often. As the size of the chamber increases, the time it takes for the balls to criss-cross the chamber must also increase. So, they cannot hit the wall as often. Thus, as the wall moves further and further back, the pressure on it must decrease. The wall eventually stops moving, at the point when the internal pressure has become exactly equal to the external (constant) pressure.

Probably the most common constant-pressure phenomena in everyday life are those affected by the Earth's atmosphere, which is way too massive to have its pressure changed by anything humans can do. (The Sun is more influential -- the weatherman's "barometric pressure" is just a fancy phrase for atmospheric pressure, and this does vary slightly with the weather.) A party balloon, for example, has constant atmospheric pressure acting on it. If you blow up a party balloon and place it in the freezer for an hour or so, it will shrink. If you let it warm up, it will expand again.

Summary

The ideal gas law is very intuitive, if you just remember what the terms in the equation represent physically and keep in mind the picture of small atoms racing about.

For a constant volume, changing the temperature (the speed of the atoms) will change the pressure because the atoms now strike the unmoving walls more (or less) vigorously.

For a constant pressure (like that provided by the weight of a movable plunger) you again change the temperature/speed of the balls, but in this case the walls are now free to move and do so, changing the distance the atoms must travel between hits. The system will come to equilibrium at a new volume, determined by the point at which the internal pressure once again equals the external pressure.

For a constant temperature, changing the volume will change the pressure (change the number of "hits" on the walls) because now the atoms have a different distance to travel and thus can strike the walls more (or less) frequently, even though their speeds have not changed.




More on Work/Energy - Carefully study each animation

Potential and Kinetic Energy Activity and the Conservation of Energy:

Instructions:

1. When the activity IN THE LINK ABOVE appears, set

  • inclined plane angle to 45 degrees;
  • height of ball to 10 m;
  • Initial velocity of ball to 0;
  • mass of ball to 1 kg and
  • delta T to 0.05

2. Set the x-axis box to x pos. (m). The y-axis box to Potential E (J) (energy in joules or m squared per seconds squared). You will be looking at potential energy....

  • Click go and notice the graph (Describe what you saw and then interpret what it means in words.)
  • Change the y axis box to Kinetic E (J) and click go. You will be measuring what happens to the kinetic energy. (Describe what you saw and then interpret what it means in words.)
  • Change the y axis box to Total (E) (J) and click go. You will now be looking at the total energy of the system. Total energy is the total kinetic and potential energy in the system. (Describe what you saw and then interpret what it means in words.)
  • Change the y axis box to x accel. (m/s/s) (Acceleration) and click on go. You will be looking at what happens to the acceleration. (Describe what you saw and then interpret what it means in words.)
  • Describe how this activity relates to the conservation of energy.

 

 

 

 

Discuss how the transfer of energy as heat is related to changes in temperature

Temperature vs Heat

Specific Heat

Latent Heat --application to weather

 

Describe the methods of heat transfer by conduction, convection, and radiation and provide examples for all

Radiation - atmosphere

Conduction- atmosphere

Convection- atmosphere

Relation to Earth's Interior- Introduction

Earth Systems: Conduction- Earth's interior

Earth Systems: Convection- Earth's interior

Earth Systems: Radiation- Sun and Earth

 

 

Explain how chemical potential energy in fuel is transformed to heat

Forms and Sources of Energy- in depth discussions

Review the carbon cycle to see how fuel is turned into different forms of energy (kinetic, potential, heat, etc.) Then return to this page.

Renewable sources

Energy Changes-general

Geothermal energy-

Design and explain experiments to induce a physical change such as freezing, melting, or boiling

Introduction to Solids, Liquids and Gases --Read up to "Smaller than Atoms"

Phases of Matter- including surface tension, viscosity and phase changes. The "designing" part of experiments refers to understand why a substance changes from a solid to liquid...a liquid to a gas. What those preparing for exams must know is the molecular basis of WHY these phase changes occur. See latent heat above (as well as specific heat) if you haven't reviewed these concepts. Then study the graphs, figures and tables to help you visualize what is happening on a molecular level.

Molecular basis of phase transitions: In the phase transition diagram in "Phases of Matter" above, there are three increases in temperature and two areas where the temperature remains constant. Using water as an example, the increase at the lower left of the curve is due to energy heating up the molecules of ice, causing them to increase in movements (specific heat of ice is a set amount of energy required to raise the temperature of ice by 1 degree C.)

This continues until the temperature reaches the melting/freezing point (0 C). At that point the curve becomes horizontal... there are no increases in temperature. This is the latent heat of fusion. Large amounts of energy are required to break the hydrogen bonds between the molecules of water in the ice. The reason that there is no temperature increase is because all the energy goes to break the hydrogen bonds... NOT to increase the movement of the molecules.

Once all the hydrogen bonds are broken and the water molecules are now free to move, further addition of energy, in the form of heat, continues to increase the motion of water molecules. The temperature rises. This is the specific heat of water... a specific amount of heat required to raise the temperature of the liquid by 1 degree C. This is called the specific heat of water. Now another horizontal area of the curve is achieved when the temperature arrives at the boiling point (varies according to altitude).

There is a longer time of horizontal graph (meaning no temperature increase), because now all the energy is going in to break the final hydrogen bonds between water molecules. This is the latent heat of vaporization or condensation. Its set value is much higher than the latent heat of ice at 0 C. After all the bonds are broken, the temperature takes another rise. This is the specific heat of steam (water molecules free in air like other molecules). There is a set value of energy required to raise the temperature of steam by 1 degree C. It is called the specific heat of steam. The motion of the steam molecules increases and so does their temperature. This is the basis upon which pressure cookers and autoclaves are based.

 

Distinguish between physical and chemical changes and provide examples of each

Review and practice- about physical and chemical properties and changes

Another practice- mainly about physical and chemical changes

 

 


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