# The Physics of Heat

## Objectives:

When you have completed this lesson and the homework, you will be able to:

• understand and define what is meant by the term phase

• understand and apply the theory of phase transitions to problems involving melting and boiling.

• combine these concepts with the previous concepts of heat capacity to solve more complicated problems.

• interpret graphs of temperature vs. heat added to a system.

In this lesson we will address the following standard from the Indiana Academic Standards for Physics I:

 P.1.3 Describe and apply the kinetic molecular theory to the states of matter. P.1.27 Understand that the temperature of an object is proportional to the average kinetic energy of the molecules in it and that the thermal energy is the sum of all the microscopic potential and kinetic energies. P.1.28 Describe the Laws of Thermodynamics, understanding that energy is conserved, heat does not move from a cooler object to a hotter one without the application of external energy, and that there is a lowest temperature, called absolute zero. Use these laws in calculations of the behavior of simple systems.

## Introduction

When you put a pot of water on the stove and turn on the burner, heat is added to the water.  As a result, the temperature increases.  After a while, however, the water starts to boil and a strange thing happens: even though the burner is on high, the temperature is no longer increasing!  It just sits there, boiling away.  So, where is all that heat energy going?  To understand what is happening, we must look at the physics of phase transitions.

## Heat vs. Temperature Graphs

Earlier we studied what happens to an object as heat is added. We learned that as heat is added, the kinetic energy of the individual molecules increases and the temperature rises.  Not all materials are the same, however.  They have different heat capacities.   450 J of heat may warm up a kilogram of iron a whole degree, but the same heat will change the temperature of a kilogram of aluminum only 1/2 of a degree.   But regardless of the amount of heat, it is always true that adding some heat to a body increases it temperature.  We can represent this by graphing the Temperature vs. Heat Added for a kilogram of the substance.

Since Iron has a smaller capacity for heat, the same amount of heat makes it change temperature more.  If something has a huge capacity for heat, then you could all lots of heat and the temperature would barely change.  The dotted red line shows how water, which has a very high heat capacity, compares to iron and aluminum.

It is important to understand this graph before we can talk about phase transitions.

## Phase Transitions

Let's take a look at what happens in the case of water.

Let's say we start with some water in a big pan that has a lid, and for the purposes of this "thought experiment" let's pretend that none of the steam is able to escape.  A thermometer is sticking out so we can see what the temperature is doing.  The burner is turned on high so heat is constantly being added to our system: Here is what happens:

1. We add heat and the temperature increases.  This continues until our thermometer reaches 100 °C.
2. Once we reach 100 °C, the temperature no longer rises.  It remains at 100 °C.  The water continues to boil, and we observe that lots of steam is produced.  The level of the water decreases.
3. Finally all the water is gone and our special pan is filled with steam that is 100 °C.  But now the temperature is going up again.  It started at 100 °C, but as the heat is added, the temperature increases.

If we were to graph what was happening, it would look something like this:

You can see that the temperature stalled while the water was being converted to steam.  This conversion from water to steam is known as a phase transition.

A phase transition is the process of changing states.  This occurs anytime a substance undergoes a change in its state, such as from a solid to a liquid (melting) or from a liquid to a gas (boiling).

As you probably can tell from the example above, phase transitions require energy.  Liquids do not naturally turn into gasses: it requires energy, in the form of heat, to get a pot of water to boil and turn into steam.   While it is in the process of boiling, the energy going into the system does not change the temperature, but is diverted to breaking the attractive bonds that keep the water molecules together.  Once these attractive bonds are broken the water molecule is free and becomes a gas.

After all the molecular bonds have been broken by the energy we are adding, then we have a pot full of gas (steam) and if we continue to add heat, the temperature will once again rise.

The previous graph is not really the whole story, however, because water also undergoes a phase transition ( a change of state) at 0 °C.   At this temperature it turns from a solid into a liquid.  The full graph of the behavior of water would look like this:

Let's summarize some important points so far:

1. The states of matter are solid, liquid and gas
2. Anytime a substance changes from one state to another, it is called a phase transition
3. Phase transitions require energy.
• To go from solid to liquid (called melting) , or from liquid to gas (called boiling) require us to add energy to break the bond that hold the molecules together.
• To go from gas to a liquid (called condensing) or from a liquid to a solid (called freezing) requires energy to be removed
4. While phase changes are occurring, the temperature of they system remains at a constant.

## Melting and Boiling Points

All substance are different, and respond to heat differently.  4186 J of energy will only heat a kilogram of water 1.0 °C, while the same amount of heat will warm up a kilogram of gold 23 °C.   It is not too hard to imagine that the temperature at which substances boil is different too.  Thanks to the work of many careful scientists, we can now look up the melting and boiling points for almost all known substances.  A few of the more common ones have been collected in a table for you:

Table of Melting and Boiling Points for Common Substances

Almost all substances will eventually freeze, if we can get them cold enough. (Helium is the exception).  All substances will eventually melt, too, if we can get them hot enough.  Since our normal earthly temperature is around 20 °C, substances with a melting point that is higher than 20 °C are generally known to us as solids.  If the boiling point is below 20 °C, we generally know them as a gas.

 Try this: What is the boiling point for Silver?

## Latent Heats

It will also not surprise you to learn that the amount of heat needed to convert a kilogram of a substance from a liquid to a gas is different for different substances.  For example, it will take 333,000 J of heat to convert 1 kilogram of H2O from ice to water.  This occurs at 0 °C.  On the other hand, if you had some ethyl alcohol that you were trying to boil, you would need 104,000 J of heat to convert it from a solid to a liquid.  To find how much heat is needed to convert a particular substance from one state to another, we can use the simple relationship

 Solid/Liquid Transitions (fusion) Liquid/Gas Transitions (vaporization) If you are melting or freezing a substance, we use Lf.  This constant is called the latent heat of fusion.  In addition, if the substance is freezing (liquid to solid) , heat must be removed, so we must put a negative sign on Q.  If the substance is melting, heat must be added, so Q will be positive. If you are boiling or condensing a substance, we use Lv.  This is called the latent heat of vaporization.  If the substance is condensing (gas to liquid), heat must be removed, so Q will be negative.  If the substance is boiling (liquid to gas) then Q will be positive, because heat energy must be added.

The constants Lv and Lf are given in the table along with the melting points for most common substances.

## Example Problem

To help put this all together, let's solve an example problem:

Problem: How much heat is needed to completely boil 1.00 Liter (1 kg.) of water that is initially at room temperature?

Solution:

Here is our plan to solve this problem

1. We first need to determine the amount of heat needed to raise the temperature of the water from 24 °C (room temperature) to the boiling temperature of water, which is 100 °C.  (This value can be obtained from the data in the Table). To do this, we will use Q = mcDT.

2. We need to find how much heat is needed to convert our water from liquid to gas.  For this we will use Q = mLv

Okay, let's give it a try:

1. First, we calculate the heat needed to warm up the water from room temperature to the boiling point.

2. Next, we determine the heat needed to completely convert the water from liquid to gas

So, the total heat needed will be the sum of the heat needed to heat up the water to the boiling point and the heat needed to change it from a liquid to a gas.

 Your turn: what is the total heat needed for the above problem?

## Summary

Everything you need to know is right here .....

 When a substance is changing temperature, we calculate the heat using When a substance is changing phase, we calculate the heat flowing into or out of it using
• If the substance is melting, we use Lf , and if the substance is freezing, we still use Lf  but we make it negative since heat must be removed to make it freeze.

• If the substance is boiling, we use Lv , and if the substance is condensing (from a gas to a liquid), we still use Lv  but we make it negative since heat must be removed to make it condense.

This is the end of the lesson. You can return to the unit main page or start the homework assignment