# Heat and Energy Transfer

There are a lot of misconceptions about heat, cold, temperature, and energy. We'll take the next few lessons to try and place some of these things in perspective. First, we need to talk about heat. We used to think that heat was a substance called "caloric". We were wrong. We do know that heat flows spontaneously from an object of high temperature to an object of lower temperature. It will never flow the other way (at least, not without some help). And there is nothing called "cold" that flows from an object of cold temperature to one of higher temperature. So get that thought right out of your head.  Some definitions:

calorie (c): A common unit of heat still used today. It is the amount of heat needed to raise 1 gram of water 1 oC  (specifically between 14.5 and 15.5 oC)

kilocalories - 1000 calories. More commonly used - heat to raise 1 kg of water 1oC.

Calorie - Also a kcal. Unit for dietary calories. How many calories are there in one of these?

BTU - British Thermal Unit. Heat to raise 1 lb of water 1 oF. 1 BTU = .252 kcal = 1055 J.

We can blame James Prescott Joule for showing that heat was a result of a transfer of energy and for finding the Mechanical Equivalent of Heat. He found

4.186 J = 1 cal, or 4186 J = 1 kcal

To sum up, heat is a transfer of energy from one body to another because of a difference in temperature between the two. The transfer will spontaneously (by itself) take place from the higher temperature object to the lower temperature object. The SI measure will be the Joule.

Thermal Energy or Internal Energy (U) is the sum total of all kinetic energy in all the molecules in a substance. These differ from Temperature, which is the measure of the average kinetic energy of individual molecules. These are still different from Heat (Q) which is the transfer of energy from one object to another because of a difference in temperature. There are some useful formulas. The internal energy of a gas is given by the formula:

where n is the number of moles of gas and R is the universal gas constant. Don't confuse this with the formula for average kinetic energy of a gas molecule (although the two are related).

A Short Trucker's Guide to Internal Energy

There is often confusion between the formula for Internal Energy of a gas and the formula for Average Kinetic  Energy of a gas molecule. The lesson on Gas Laws defines Average Kinetic Energy as

and this lesson further confuses us by defining Internal Energy as

They look pretty similar, and it is easy to pick the wrong formula when doing problems if we have a misconception of what we are working with. 3/2 is common to both, as is the temperature in Kelvin (T). So while the next few statements may seem like they go without saying, trust me - it's well worth looking over this simple derivation.

Internal Energy is the sum of all of the average kinetic energies of the molecules in a gas. Does that make sense? Remember in basic mechanics, we find the total energy of a system by adding all the individual energies of the components of the system? That's what we are doing here. Let N = number of gas molecules in the system (our number of "objects".) Then,

Remember also that we defined the Universal Gas Constant, R, which gives us the amount of energy in a gas for  each mole of the gas per degree Kelvin (Joule/mol-K). We also defined Boltzman's Constant, k as the energy of a single molecule of gas per degree Kelvin (Joule/K). Boltzman's Constant is just the Universal Gas Constant divided  by Avagadro's Number, or

k = R/Na

So let's go back to the Average Kinetic Energy and make the substitution for Boltzman's constant:

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More Substitution:

But we recall that the number of moles of a gas (n) = N/Na, so making one last substitution:

Practice this until you can do it yourself, or at least until you believe that this is where it comes from.

The heat (Q) required to change the temperature (DT) of an object is given by the equation:

where c is a quantity called the specific heat. Specific Heat is unique for each material, and the SI units are kcal/kg-oC or J/kg-oC. Values for c can be found in various tables. Variations include

cp - the specific heat of gases at constant pressure, and

cv - the specific heat of gases at constant volume.

We use a process called Calorimetry to find the specific heats of various substances. Calorimetry works because of the law of Conservation of Energy, which tells us that Heat Lost = Heat Gained when two substances are brought together. We use Calorimetry to measure the exchanges of energy.

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http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html (Specific Heat)

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html (Heat and Kinetic Energy)