Measurements and Standards
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:
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:
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.
Molecular Expression of Temperature
Temperature is in direct proportion to average molecular kinetic energy:
where kB is Boltzmann's Constant.
The latter equation is a mode of expressing kinetic energy of particles in terms of thermodynamics.
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.
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.
Then we can find the heat energy:
Q is often expressed in Joules or Calories
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:
Calculating one of these variables under the assumption of conservation of (thermal) energy is often termed calorimetry.
There are generally two kinds of latent heats caused by phase changes.
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:
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.
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:
The efficiency, e, of the heat engine is a ratio:
and we know W in terms of Q as well...
Carnot showed this in terms of temperature (in Kelvin temperature scale):
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.
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