So over on this side, we'll have the definition of heat capacity, regular heat capacity, is the amount of heat you add divided by the change in temperature that you get. So on this side we're adding heat, let's say heat goes in, but the piston does not move and so the gas in here is stuck, it can't move, no work can be done. Since this piston can't move, external forces can't do work on the gas, and the gas can't do work and allow energy to leave.
Q is the only thing adding energy into this system, or in other words, we've got heat capacity at constant volume is going to equal, well, remember the first law of thermodynamics said that Delta U, the only way to add internal energy, or take it away is that you can add or subtract heat, and you can do work on the gas. So there's no work done at all so the heat capacity at constant volume is going to be Delta U over Delta T, what's Delta U?
Let's just assume this is a monatomic ideal gas, if it's monatomic we've got a formula for this. That's not the only way I can write it.
Remember I can also write it as three halves NK Delta T over Delta T, and something magical happens, check it out the Delta T's go away and you get that this is a constant. That the heat capacity for any monatomic ideal gas is just going to be three halves, Capital NK, Boltzmann's constant, N is the total number of molecules.
Or you could have rewrote this as little n R Delta T. The T's would still have cancelled and you would have got three halves, little n, the number of moles, times R, the gas constant. So the heat capacity at constant volume for any monatomic ideal gas is just three halves nR, and if you wanted the molar heat capacity remember that's just divide by an extra mole here so everything gets divided by moles everywhere divided by moles, that just cancels this out, and the molar heat capacity at constant volume is just three halves R.
So that's heat capacity at constant volume, what about heat capacity at constant pressure? Now we're going to look at this side. Again, we're going to allow this gas to have heat enter the cylinder, but we're going to allow this piston to move up while it does that so that the pressure inside of here remains constant and this is going to be the heat capacity at constant pressure.
What's W going to be? Remember W is P times Delta V. So this is a way we can find the work done by the gas, P times Delta V, so this is going to equal Delta U, we know what that is. If this is again, a monatomic ideal gas, this is going to equal three halves nR Delta T plus this is P times Delta V, but we have to be careful, in this formula this work is referring to work done on the gas, but in this case, work is being done by the gas, so I need another negative.
Technically the work done on the gas would be a negative amount of this since energy is leaving the system. So what do we get? Look what I'm left with. I'm left with C. Heat capacity at constant pressure is going to be equal to three halves nR plus nR, that's just five halves nR, and if I wanted the molar heat capacity again I could divide everything, everything around here by little n, and that would just give me the molar heat capacity constant pressure would be five halves R.
And notice they're almost the same. The heat capacity at constant volume is three halves nR, and the heat capacity at constant pressure is five halves nR. They just differ by nR. So the difference between the heat capacity at constant volume which is three halves nR, and the heat capacity at constant pressure which is five halves nR, is just Cp minus Cv which is nR, just nR, and if you wanted to take the difference between the molar heat capacities at constant volume and pressure, it would just be R.
The difference would just be R because everything would get divided by the number of moles. So there's a relationship, an important relationship. It tells you the difference between the heat capacity at constant pressure and the heat capacity at constant volume. Use Cp when there's constant pressure.
This is the specific heat when there's constant pressure. The Cp and Cv for ideal gases can be found on Lavelle's equation sheet on his website. Cp Post by Julian Krzysiak 2K » Mon Jan 22, am Cp is the heat capacity for something at a constant pressure, and would be equal to Cv is the heat capacity for something at a constant volume, and would be equal to You'll know when to use a particular heat capacity because they'll specify in the problem the conditions of the reaction, or you'll have to infer the conditions, for example, when there is an open container, it will have to be at a constant pressure of 1atm.
You usually use these equations when dealing with anything in calculating how much heat was given off, the change in temperature, or any variation in dealing with is the specific heat capacity for something at a constant pressure in terms of moles is the specific heat capacity for something at a constant pressure in terms of grams So you'll have to use either one depending in which units they give the amount to you, or if given enough information, you could convert grams into moles, vice versa, and then use which equation you want.
Cp is for constant pressure. Now let us uh make this process on the PV background. So this is the isolated process here. You can see that this is a pressure And this is State one stage 2.
And at ST one the pressure is P. One and at ST to the pressure is Peter which is equal to P one because This is a hold on the line the pressure remains constant. So both pressure at the point that the pressure. So that is why we say that is an isil barrick process. And now next we wrote an example for this process. So you can consider this questions linger arrangement. This is christian here. And this question is movable. So and this gas inside the cylinder.
And we are increasing the temperature by using any bono you can take Now this uh the temperature is going to increase. Center question is mobile. It was going to ask. This question will move in the upward direction so that the volume increases. But the volume will increase, temperature will also increase but the pressure will remain constant. So this is example for the isometric process. Next finally will define the eyes aquatic process.
So the ice aquatic process, this means the constant volume process. That means the volume will remain constant during the process.
So let us make the PV diagram of this process. So there's a PV diagram, This is State one, stage two. And during this process the volume remained constant, the volume at. That is equals to be next.
We hear a little example for the is a correct process. So again we can take this questions in the arrangement but this time this question is not movable, it is fixed, it is fixed at this position. And similarly we have the gas inside the cylinder and we are increasing the temperature of the gas by using bono. Now, this time the temperature we're going to increase. But since the question is fixed here, the volume will not going to increase because it will not be moving in the up for direction.
It is fixed here. So volume and temperature increases, pressure also increases, but volume remained constant, so volume is constant. So this example for the eyes aquatic process. So there's a final answer. I hope you have understood all the four parts. Thank you so much. Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds.
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