# Pressure and number of moles relationship quiz

### Ideal Gas Law - ProProfs Quiz

Perfect prep for Review of Gases quizzes and tests you might have in school. What is the correct relationship between vrms,, and vp? An isolated container of gas doubles in pressure and triples in volume. . A sample of gas has a volume of L at a temperature of K. How many moles are in the sample? ; If temperature is constant, the relationship between pressure and volume is A quantity of gas has a volume of liters at °C and atm of pressure. . A gas of 1 mole has a temperature and volume at STP, the temperature of the . c. moles. d. volumes. ______ 4. The volume of 1 mol of any gas at STP is a. Which law implies that the volume of a gas is directly proportional to a. pressure, volume, temperature, the gas constant, and number of moles.

That's what the heat capacity tells you. So capital C is heat capacity and it's defined to be the amount of heat that you've added to the gas, divided by the amount of change in the temperature of that gas.

And actually, something you'll hear about often is the molar heat capacity, which is actually divided by an extra n here. Pretty simple but think about it. If we had a piston in here, are we going to allow that piston to move while we add the heat, or are we not going to allow the piston to move? There's different ways that this can happen, and because of that there's different heat capacities. If we don't allow this piston to move, if we weld this thing shut so it can't move we've got heat capacity at constant volume, and if we do allow this piston to move freely while we add the heat so that the pressure inside of here remains constant, we'd have the heat capacity at constant pressure.

And these are similar but different, and they're related, and we can figure them out. So let's clear this away, let's get a nice, here we go, two pistons inside of cylinders.

We'll put a piston in here, but I'm going to weld this one shut. This one can't move. We'll have another one over here, it can move freely. 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? I then pass out the quiz to students. I have two versions of the quiz to ensure academic honesty and give them so that students have a different version from the person next to or across from them.

This is a copy of the quiz. As students complete their quizzes I have them turn over and then come around to collect. I give students about 10 minutes to complete the quiz. When students are done if I have collected their quiz then I encourage them to get out their binders and begin to get ready for the lesson.

After class I grade the quizzes using the answer key and place in my gradebook.

See the attached reflection for more details about how I do quiz corrections. I begin the lesson with teaching students about the Ideal gas law on slide 2. I also tell students that there are multiple "R" values, but that for this class we will only be using 0. There's just little particles in here. And what you're actually feeling are these particles striking your hand, so your hand's just getting bombarded by these particles. But they're so small and they're so many of them, you can't really tell that there's particles.

It just looks completely continuous. So for Boltzmann, this heat energy isn't really a new kind of energy at all.

### Gas Laws Quiz - By maroolat

All this is, this heat energy that you're feeling is just kinetic energy, and if it's steam, it's just the kinetic energy in the H2O molecules flying around in here at some rapid speed. And the faster they go, the greater the impact with your hand, which is gonna transfer more energy. So the faster they go, the hotter it feels in here. So, for Boltzmann, to say that something has a high temperature, if you said that the temperature is large, if it's hot outside, that's kind of redundant.

We already had a word for that.

## Boltzmann's constant

We could just say if it's a high temperature, what we really mean is that the average kinetic energy of the gas molecules outside is large. So, if a gas has a high temperature, the average kinetic energy of those molecules is large. That's why it hurts when they impact on your skin 'cause they're transferring kinetic energy to the molecules in your hand, and when your hand absorbs too much energy, these molecules move around, your skin starts to get damaged, you can get burned.

So this is often referred to as the kinetic-molecular explanation of temperature. And the details of this theory were one of Ludwig Boltzmann's biggest contributions to science. But what does any of this have to do with Boltzmann's constant? Well, let's get rid of all of this. You've probably heard of the ideal gas law, PV equals nRT.

So, remember, T is the temperature measured in Kelvin. P is the pressure, and I'm gonna measure this pressure in, I'm gonna choose to measure it in Pascals.

V is the volume, I'm gonna choose to measure it in meters cubed. And n, little n, remember, little n is the number of moles of the gas. And if you've forgotten what moles are, n, the number of moles, is defined to be capital N, the number of molecules in the gas, the total number of molecules in the gas, divided by a constant and that constant's called Avogadro's number.

And if you've forgotten Avogadro's number, Avogadro's number is 6. So in every mole of a gas, what we mean by one mole of a gas is 6.

And if you choose these units, this R, this gas constant, R is called the gas constant, and it has a value, R has a value of 8. That's the gas constant R with these units. But these are pretty macroscopic quantities, pressure and volume and temperature and moles. Even moles, talking about one or two moles is talking about a huge number of molecules.

You're kinda glossing over some of the microscopic details, so an alternate way to write the ideal gas law is P times V equals capital N, so forget moles. Let's say we want to talk about how many molecules there are.