Topic Elements

Review Material

Formulas
Calculator
We start off assuming you have basic knowledge in chemistry in pressure-temperature-volume relationships (Ideal Gas Law)

 P1V1 = P2V2 T1 T2

 PV = nRT = NkT

Terms:

• iso--equal; remains constant
• isothermal--constant temperature
• isobaric--constant pressure
• isochoric--constant volume
• adiabatic--no heat gain/loss in the system

Kelvin and Celcius Temperature Scales

Celcius we all know, though you maybe also familiar with the Fahrenheit temperature scale.

Since most equations, and most standards, are dealt in Celcius or Kelvin form, conversion from Fahrenheit to Celcius could be useful:

 F = (9/5)C + 32 F = Temperature in Fahrenheit; C = Temperature in Celcius

But anyway, now down to the nitty-gritty stuff. Using a gas thermometer, we can find temperature via pressure variation of a fixed volume of gas. These pressures and temperatures measured are then plotted on a graph of P versus T. We do this for several gases and find their linear relationships.

But in this graph, there is no temperature for which pressure is 0. Where temperature is zero, motion of particles would cease completely, so as to not bounce off surfaces to create pressure.

So since we seem to have a linear relationship between P and T, we can extend the lines back until they intersect  the T axis. Surprising, or not, they intersect at the same point, which we call absolute zero.

The Kelvin temperature scale, [Kelvins] = K, developed by William Thompson, is the equivalent of saying that -273º C = absolute zero = 0 K. Therefore:

 C = K + 273

Now, when you vary the heat in certain materials, there is thermal expansion of the material. That is, it will expand according to the temperature the material is placed in. That is why buildings and sidewalks have to compensate for the expansion or contraction of materials.

 /\L = a Linitial/\T Linear Expansion /\A = L2 = yAinitial/\T Area Expansion (y = 2a) /\V = L3 = BVinitial/\T Volume Expansion (B = 3a)

Molecular Expression of Temperature

Temperature is in direct proportion to average molecular kinetic energy:

 T = 2mv2 3·2kB

thus,

 1 mv2 = 3 kBT 2 2

where kB is Boltzmann's Constant.

The latter equation is a mode of expressing kinetic energy of particles in terms of thermodynamics.

Joule's Experiment

When an object is in motion, we notice that it loses mechanical energy from friction. Well, James Prescott Joule was the first to show that energy is converted into another form in his famous experiment. This other form was thermal energy.

Specific Heat

So friction and other mechanical energies increase the temperature of the water (as in Joule's experiment). Now that we have established that it has been proved, we might want to be able to calculate the actual changes in temperature from mechanical energy.

The heat energy required to raise a fixed amount of a given substance varies for each substance. Let's think of it this way:

If you add a certain amount of heat energy, which we call Q, into a substance, then you get a certain temperature change depending on the mass of the substance affected.

Therefore, each substance has a unique specific heat, which we label as c.

 c = Q m/\T

Then we can find the heat energy:

 Q = mc/\T

Q is often expressed in Joules or Calories

 J = cal

Table of Specific Heats of Some Materials at Atmospheric Pressure
 Substance J/(kg C) cal/(g C) Aluminum 900 0.215 Beryllium 1820 0.436 Cadmium 230 0.055 Copper 387 0.0924 Germanium 322 0.077 Glass 837 0.200 Gold 129 0.0308 Ice 2090 0.500 Iron 448 0.107 Lead 128 0.0305 Mercury 138 0.033 Silicon 703 0.168 Silver 234 0.056 Steam 2010 0.480 Water 4186 1.00

Conservation of Energy

Q is a form of energy; it is heat energy. And since it is energy, we can assume it is conserved. Mechanical energy is conserved, and upon showing the equivalence between mechanical and thermal energy, we can express this thermal conservation as:

 Q1 = Q2

 (mc/\T)1 = (mc/\T)2

Calculating one of these variables under the assumption of conservation of (thermal) energy is often termed calorimetry.

Latent Heat

 Q = mL

There are generally two kinds of latent heats caused by phase changes.

• Fusion [Q = mLf]
• Vaporization [Q = mLv]

From the flat parts we see that heat is added to the water but there is no actual temperature rise. These horizontal sections are when the water undergoes phase changes. Phase changes require energy to convert the water into a different form, hence the lack of temperature change. This is an example latent heat.

Whenever the material (such as water) experiences a phase change heat is added in but there is no temperature change in the outcome, however, always figure in latent heat when solving the problem if there is a known phase change occurring somewhere in there.

Work and Heat

Well, there is an equivalence between mechanical energy and heat energy. Work can be expressed in terms of pressure, area, and displacement. We can look at a contraption such as a piston to explain it:

 W = Fd = PAd = P/\V

where P = pressure, A = area of the surface, d = displacement, and /\V = change in volume due to the displacement. There is another way of looking at work; we can consider work equal to the difference between the heat in and the heat out, embodied in the 2nd law of thermodynamics.

P and V? Those are components of the ideal gas law...yeah so lets take the sure-fire approach; graph them

Since we know that PV is the work done, we know that graphically, work is the area under the curve...or simply line, in this case. This is the work done by a gas in one state to another. ("state" meaning from one initial set of P and V to another [final] set of P and V)

The Zeroth Law of Thermodynamics

If two materials are, in themselves, in thermal equilibrium, with a third material, then the two materials will be in thermal equilibrium with each other if they are put in thermal contact*

In other words, if one material is in equilibrium with a material, A, and another material is in equilibrium with A, then the two materials will be in equilibrium with each other if put together. A logical step.

The First Law of Thermodynamics

This is another form of conservation of energy and this time takes into account friction and heat energies. And thus can keep these factors in evaluating the situation. Friction, which had been thought to be a nonconservative force is actually conserved.

 /\U = Uf - Ui = /\Q - /\W /\Q = /\U + /\W

where /\U is the change in the internal energy of the system, /\Q is the change in the thermal energy of the system, and /\W is the work done by the system.

The Second Law of Thermodynamics

In machines, as in the section on simple machines and in life, we won't find nice 100% efficiency that would be in an ideal world. When a machine is used, there is always a heat loss, most likely due to friction.

The second law of thermodynamics is an explanation developed for the Carnot heat engine. The important concepts here are that:

• at maximum, a heat engine can be only 85% efficient
• heat engines operate in terms of hot/cold reservoirs (obviously the hot reservoir is in a state of higher temperature than that of the cold reservoir)
• heat flows from hot to cold (concept of entropy)
• the net work done by the heat engine is the net heat flowing into it: Wnet = Qhot - Qcold

The efficiency, e, of the heat engine is a ratio:

 e = W Qhot

and we know W in terms of Q as well...

Carnot showed this in terms of temperature (in Kelvin temperature scale):

 e = Thot - Tcold Thot

Convection

Convection results when a heated substance transfers its heat by movement.

Heating by Convection: Say there is a source of heat, as in a fire. The air above the fire is heated by it and as a result expands, losing density, and thus the air rises, like the heat waves we see in hot summer days. This air feels hot to us as it passes around our bodies. We feel it because it is transferring some of its heat to us when the air is in contact with our skin.

[Back to the Top Practice Questions]
Key Themes
• Terms
• Temperature Scales
• Thermal Expansion of Solids and Liquids
• Joules Experiment
• Specific Heat
• Conservation of Energy Qi = Qf
• Latent Heat and Phase Changes
• Work and Heat
• Laws of Thermydynamics
• Practice Questions

Java Interactions and Demonstrations

• none