Chapter 15: Temperature, Heat, and Expansion

Are temperature and heat the same thing?

No. Before we get into the difference let's think about temperature and internal energy. Consider the animated gifs to the right. The particles move around randomly in the two images. The average energy at which the particles move defines the temperatures of the two fluids. This place-to-place motion of the particles is referred to as translational motion and this kinetic energy as translational kinetic energy.

If we cool a fluid so that all motion stops, we reach Absolute Zero. We have never reached Absolute Zero, we have gotten close, (0.000 000 000 1 Kelvin, see below for definition of Kelvin).

Temperature Scales

We measure temperature using different scales. The most common one is the Celsius Scale. In the Celsius Scale, 0 Celsisus is the temperature at which water freezes (at 1 atm) and 100 Celsius is the temperature at which water boils (at 1 atm). As we lower the temperature of a gas, the particles move with less energy. If we cool a fluid to -273.15 Celsius, then all motion stops. This is Absolute Zero.

The scale used by scientists, the Kelvin Scale, sets Absolute Zero as the zero point. In the Kelvin Scale, water freezes at 273.15 Kelvin and water boils as 373.15 Kelvin. That is in the Kelvin Scale, one degree of temperature chnage is the same as one degree of temperature in Celsius.

The temperature scale used in the United States is the Farenheit Scale where water freezes at 32 degrees Farenheit and water boils at 212 degrees Fareneheit at 1 atm. A temperature of 0 degress Farenheit is below the freezing point of water. Absolute Zero is at -460 degrees Farenheit. We see from the freezing and boiing points of water, that a change of one degreee Farenheit is smaller than one degree Celsius or Kelvin. There are 180 degrees of Farenheit change between the freezing and boiling points of water compared to 100 degrees of temperature change for the Celsius and Kelvin scales. This means that a one degree change in temperature for the Celsius and Kelvin scales correspond to 1.8 degree change in temperature for the Farenheit scale.

  • Room temperature of 68 degrees Farenheit = 20 Celsius = 293 Kelvin.
  • Surface temperature of Sun of 5,800 Kelvin = 5,527 Celsius = 10,220 Farenheit
To convert from Celsius to Farenheit and Farenheit to Celsius use:

  • Temperature in Farenheit = (temperature in Celsius) x 9/5 + 32
  • Temperature in Celsius = (temperature in Farenheit - 32) x 5/9

Pressure and Absolute Zero

Pressure

The value of Absolute Zero can be estimated from a simple experiment involving the pressure. The pressure exerted by a fluid depends on the temperature of the fluid and its density. Imagine a fluid composed of particles that are in random motion. When these particles hit a wall, they impart an impulse to the wall (they push on the wall). In a box that contains many particles, the rate of impacts every second is large. The total impulse delivered to the wall, the pressure exerted on the wall, is determined by the number of impacts on the wall (determined by the number of particles in the particles in the box) and the impulse that each impact carries (determined by how hard the particles hit the wall which is determined by how much kinetic energy each carries which is determined by how fast they are moving and their mass). The measure of the average translational kinetic energy of a particle is the temperature of the fluid.

The pressure exerted depends on the density of the fluid and the temperature of the fluid.

When the fluid is at Absolute Zero, the pressure of the gas should go to zero.

Heat

When we immerse the pressure gauge into each fluid (each maintained at different temperature), the pressure gauge and the bath exchange energy in the sense that heat flows from the hotter object to the cooler temperature. Energy flows until the two objects reach the same temperatures and attain theraml equilibrium.

This is what we mean when we refer to Heat. Heat is the energy that is transferred between two objects with different temperatures.

Heat is measured in Joules, the kinetic energy of a 1 kilogram object (1 kilogram is 2.2 pounds on the surface of the Earth) moving at speed 1 meter per second (3.6 kilometers per hour). A more accessible unit is the calorie. One calorie is the heat input needed to increase the temperature of 1 gram of water by one degree Celsius. The more common energy measure (the one associated with different foods) is actually the Calorie, the heat input needed to raise 1 kilogram of water by one degreee Celsius. One Calorie = 1,000 calories.

What are the Internal Energy and Heat Capacity?

In the discussion of temperature and Absolute Zero, the temperature of the fluid (and the relationaship of the pressure to the temperature), is based on the energy of the particles as they move from place-to-place in the fluid. This place-to-place motion determines the temperature of the fluid. There can be more energy associated with the fluid, however. For example,

What goes on inside of the particles, the big red dots?

Well if they are molecules, they can spin and vibrate as shown to the left. That is, in addition to having energy associated with the movement from place-to-place (translation), there may be an energy associated with motion hidden within the molecule itself (the rotation and/or vibration). The total amount of energy in the fluid, the Internal Energy of the fluid, must include all of these energies. An important point to remember, however, is

    The temperature of the gas is determined by only the translational energy. This means that sometimes we can transfer large amounts of energy (Heat Transfer) to a fluid without changing its temperature greatly!

This ability to accept energy without raising the temperature has interesting consequences, some of which we address later. The ability to store energy is measured by the

Heat Capacity

of the material.

Heat Capacity

Heat capacity is the ability of a material to store energy. We define heat capacity as the amount of energy needed to change the temperature of a material by one degree Celsius or the amount of energy released when a cooling material lowers its temperature by one degree Celsius.

Heat capacity may be thought of as Thermal Inertia, the resistance of an object to changes in its temperature.

  • It is hard to raise the temperature of an object which has large heat capacity. Large amounts of heat transfer are needed because the heat transfer goes into increasing the internal energy of the object and so is shared between the translational motion (temperature) and things like molecular rotation and vibration (which, essentially, are hidden from us).
  • Objects with large large heat capacity can store lots of energy and so take long times to cool.

The water temperature increases less than the temperature of the ethyl alcohol for the same heat input ===> water has higher heat capacity.

Water and Other Specific Heats

The heat capacity of water is large. In a second we will present a value for the heat capacity of water. First I must make a defintion. It is clear that it will be easier for me to raise the temperature of a thimble full of water 1 degree than it would be for me to raise the temperature of the Pacific Ocean by 1 degree and the heat capacities would then, technically be different in each case. Unfortunately, this means that the Heat Capacity depends not only the fact the material in question is water, but we also need to worry about how much water there is. This state of affairs is not good when we want to define a property of water.

We can easily rectify this situation by asking a simpler question,

What is the amount of heat transfer needed to raise the temperature of 1,000 cubic centimeters of water (1 kilogram of water)?

We can use this idea to define the

Specific Heat Capacity

the heat needed to raise the temperature of 1 kilogram of water by 1 degree Celsius from a temperature of 20 Celsius, 4,184 Joules. This number is actually huge. Lead heats and cools very quickly

Demonstration: In class, we placed 170 grams of Aluminum (density = 2.7 grams per cubic centimeter), steel (density = 7.8 grams per cubic centimeer), and brass (density = 8.8 grams per cubic centimeter) into boiling water (100 degrees Celsius) and heated them.

  • When placed in ice, each melted a certain amount of ice. The amount melted ran from Al to steel to brass in terms of the amount of ice melted.
  • This indicates that Al contained more energy than steel which contained more energy than brass when equal amounts of each were heated to 100 degrees Celsius.
  • This is because Al, Steel (iron and carbon) and Brass (copper and zinc) have specific heat capacities of 910 J per kilogram per change in temperature, 490 J per kikogram per change in temperature, 380 J per kilogram per change in temperature, respectively.
  • Note that the specific heat capacites are ranked as low density to high density.

Material

Specific Heat Capacity

Air

1,010 Joules/kg/C

Aluminum

896 Joules/kg/C

Copper

390 Joules/kg/C

Human Body

3,500 Joules/kg/C

Lead

130 Joules/kg/C

Wood

1,800 Joules/kg/C

Oceans, Circulation, and Temperature

The heat capacity of water is large compared to the heat capacity of most regular materials. This has consequences for the climate on the Earth. The surface water of the ocean cools at the points indicated, gets denser, and sinks. It flows as deep water currents around the globe upwelling where indicated. Because of the high specific heat capacity of water (and the huge amount of water on the surface of the Earth, heated takes long times to shed its energy and is thus able to transport energy over large distances. This smooths temperature differences on the surface of the Earth.

Thermal Expansion

As materials are heated, the molecules gain kinetic energy and therefore tend to expand and get less dense. If they are cooled, they tend to contract and get denser. An important exception is water.
Near the freezing point of water (0 to 4 Celsius), liquid water increases in density as it rise from 0 degrees Celsius to 4 degrees Celsius. Beyond 4 degrees Celsius, liquid water gets less dense as it heats. This has real-life consequences. Note that the expansion and contraction is not huge for water as water tends to be incompressible.

Material

Linear Expansion Coefficient

Volume Expansion Coefficient

Aluminum

0.000024

0.000069

Copper

0.000017

0.000051

Iron

0.000012

0.000033

Steel

0.000013

0.000039

Glass, ordinary

0.000009

0.000026

Glass, pyrex

0.000004

0.000010

Gold

0.000014

0.000042

Tungsten

0.0000043

0.000014

Platinum

0.000009

0.000027

In the table the changes are fractional changes of the materials for every 1 degree Celsius increase of the materials if the materials are initially at 20 degrees Celsius.

Frozen Lakes

Why don't fish freeze during the winter in high mountain lakes?

During the summer, the surface temperature of a lake is something like 10 degrees Celsius, above the freezing point of water.

  • As winter approaches, the surface water cools gets a little denser and sinks to the bottom of the lake.
  • If water wasn't unusual, we see that as the surface water approaches the freezing point, it would continue to get denser as it cooled. Consequently, the coldest water would sink to the bottom of the lake and the lake would first start to freeze at its bottom. Ice would form bottom up.
  • Water is unusual, however. Below 4 degrees Celsius, its density gets smaller as it cools. It stays off the bottom of the lake. The minimum, the water below can reach is 4 degrees Celsius (where water is the densest).
  • This means that as the surface approaches the freezing point of water, the water stays near the surface and the lake freezes from the surface down. In the fact, the lake will not form ice until the entire body of water is around 4 degrees Celsius below the surface.
  • The ice layer will continue to cool and form ice so that it will thicken and works its way downward.