And that heat is just the change in internal energy. So if the specific hear is constant (it is constant for an ideal gas, not for a real gas) then at a temperature of T in Kelvin the internal energy would just be U = CT.
As I discussed above, for a monatomic ideal gas this energy is stored as the KE of gas molecules.
When you define the internal energy as U = CT it makes no reference to the velocity of the container. It's just the heat needed to heat it from absolute zero up to the temperature T. Yes?
Now, we can also define the specific heat as the KE of the gas molecules. Each molecule has an energy ³⁄₂kT so if we have one mole, i.e. Na molecules, then the total energy is U = Na k T.
And comparing this with the previous definition we see that ³⁄₂R = C i.e. the specific heat is ³⁄₂R. And you should recognise this as the value of Cv for an ideal monatomic gas.
That's why we need to use the COM frame. If the gas as a whole was moving at some speed v there would be an extra KE ¹⁄₂mv² and the energy calculated from the KE would no longer be the same as the energy calculated from the specific heat.
And the answer is that the internal energy calculated from the KE only matches the energy calculated from the specific heat if we measure the KE in the COM frame.
@Wolgwang this is a somewhat philosophical question. While questions like this can be fun to argue about mist physicists are not very interested in them.
The current notion of the scientific method is down to a philosopher called Karl Popper.
His idea is that you create a hypothesis and then you do an experiment to test it. If the experiment shows your hypothesis is wrong then you go away and create a new and improved hypothesis, then you test the new hypothesis and so on.
But suppose the experiment doesn't disprove your hypothesis, does that mean your hypothesis is true? Well not necessarily. After all there are many different experiments you could do to test your hypothesis and any one of those experiments could disprove it.
So to prove your hypothesis you'd have to do every possible experiment. Then, and only then, could you state confidently your hypothesis is true.
Well look what happened with Newton's laws. Until 1905 we thought they were always true. Then we discovered that at high speeds we get relativistic effects and Newton's laws don't apply.
So it took over 300 years to disprove Newton's laws.
Now we think quantum mechanics is true because so far it has never been disproved, but quantum mechanics is less than a hundred years old. Give it another two hundred years and who knows?
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@Wolgwang I'm not sure the terms model and hypothesis are precisely defined. I would consider them to mean much the same, but maybe philosophers of science have different definitions for them.
@Wolgwang in my unsolicited amateur opinion, i think hypothesis (which i think is synonymous with postulates) is when scientist assume/guess (in Feynman's own words) where they just guess what is most likely to happen and model is when they give a description of how the things involved
You can think of comparing and contrasting Bohr model and Bohr postulates as an example
@Wolgwang My pleasure. Also if you are more interested, i suggest looking up one of Feynman's lecture at MIT on the scientific method where he talks about how theories are made
@JohnRennie Good evening sir. Can you tell what is meant by Va- Vd in this case, with respect to the work done by the Electric field and the external force. Like from where to where?
I got the correct answer which 20V, but I am not sure if my concept is write. I simple did Work= Force*perpendicular distance with F=electrical force (cause work per unit charge is V and force per unit unit charge is E)
@AdilMohammed you've got to use force*parallel distance. you were lucky this was a square
$$\int{\textbf{F}\cdot d\textbf{l}}=W_{done}$$ the dot product signifies that the magnitude of force along the length (or the magnitude of length along the force travelled) is the work done
Problem Solving Strategies
Problem Solving Strategies