Thursday, February 11, 2021

Energy, Heat, Temperature Change, and Thermal Exchange

General Chemistry Index

Where are we going with this? This page will assist in developing the ability to perform calculations involving heat flow, temperature changes, and phase changes by using known values of specific heat, phase change constants, or both.

Energy, Heat, Temperature Change and Thermal Exchange
This doesn't sound too bad, right?

So, energy… heat… temperature change. Seems pretty easy, but…

Since science uses words in very specific ways, we need to do some work to specify what is what.

Energy—the potential to do work. In this and the associated discussions, the general understanding of energy is sort of down-played in favor of the specific type of energy to be explored, which folows.

Heat (also Thermal Energy)—Energy stored with the molecules of a substance; the sum of all the molecular kinetic energy. Usually represented by the letter Q.

Temperature—a number on one of several scales that is an indication of relative average kinetic energy of the molecules being measured.

Temperature change—a quantity that is the difference of two temperatures separated by time. Temperature is represented by the scientific symbol for change, the ∆, and the scientific symbol for temperature, T. Hence, where Tf represents final temperature and Ti represents initial temperature.

∆T = | Tf - T

Hold up! That last thing looked like math! And what… is that the absolute value things! Sheesh! I thought that was just make-believe!

So what does all that mean? Let's say there's this chunk of metal. It has a temperature. That's easy enough. Let's say it's temperature is 20°C. So, that means that the average kinetic energy of all the molecules in that chunk of metal comes to 20°C. 

The sum of all that energy is the thermal energy. You could do something with that energy. Say you put that chunk of metal into a small beaker of cool water… the water would heat up.

Now, if you think about it, the bigger the chunk of metal, the more thermal energy it can store. And the hotter it is to start with… Suppose you had a HUGE chunk of metal at 300°C. If you put that into water, it would cause some of the water to boil! All of the water would heat up!

Intuition would reveal that bigger things have more thermal energy than small things made of the same material. A pound of hot lead will heat up more water that an ounce of hot lead. Further, if something starts off hotter, it has more energy than if it starts off lukewarm.

It's also not a great leap to realize that, as the water heats up—that is to say, gains thermal energy (heat)—the chunk of metal will cool off (lose heat.)

This is heat exchange—the transfer of thermal energy from one thing to another; the higher temperature thing loses heat and the lower temperature thing gains heat.

Now, the law of conservation says that energy cannot be created or destroyed, so… THIS IS HUGE…

Heat loss = Heat gained

And… somewhere up in all those words, we said that the symbol for heat was Q, so…

Qlost = Qgained


Q- = Q+


Ql = Qg

Now, we just need to know what Q is in terms of temperature change and how much stuff we have.

Let's go with that intuition again… The hotter to start with… so if it goes from real hot to cool, more energy is given off. This is the temperature change quantity, ∆T.

More stuff has more heat… so… how do we measure "more" or less with regards to matter? Mass, which is the symbol m.

One more thing to consider… Sometimes, things at the same temperature seem to be "hotter" than others. If you have a plastic cup and a glass cup that are both the same temperature (such as if they come out of the hot sink water or dishwasher), the glass cup feels hotter. There must be some factor related to what the material is made of. 

There is.

It's called specific heat. It's just a number, but usually, it is a decimal of some sort. It is represented by the letter c.

Okay, so… how much heat does that chunk of metal have in it? If it gives off some of that heat, we can calculate the amount of heat! Very easy…

More mass = more heat!
Bigger temperature change = more heat!
Then that c thing…

Where Q is heat change, where m is mass, c is specific heat, and ∆T is change in temperature, 

Q = mc∆T

So, now it comes down to math! Really?

It's fair to think of it this way…

Q is heat (thermal energy)
m is how much stuff you have
c is what kind of stuff you have
∆T is how much did the temperature of the stuff change  

The good thing about this is all you do is multiply and divide.

That's enough for now. In other articles, the idea of heat exchange will be looked at more closely and more precisely. And, naturally, there will be examples.

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