Everyone, hopefully, you guys tried this practice problem. It's a pretty classic barometer problem. We've got a barometer here that is 1 meter tall, so that means this distance here is 1.0 meters. Now, normally, this height never really matters, the height of the actual tube itself, and it's filled with mercury. So in other words, this liquid here is going to be mercury. Remember that the density of mercury, which is given by the chemical symbol Hg, is equal to 13,600 kg/m3. It might be a good thing to memorize, because it's a pretty common one. What we want to do is we want to calculate the atmospheric pressure in atm. So in other words, the atmospheric pressure that's pushing down on the open part of the barometer. So this is going to be your PATM. In other words, this is going to be your atmosphere, the air pressure, however you want to think about this, but we want to calculate this in atm.
Alright. So how do we do this? Well, if you have the column of liquid that is 76 centimeters high, then that means that this piece right here, this height, is going to be 76 centimeters or 0.76 meters. Remember, if you ever have a column of liquid that you can measure like this, then you're usually going to have to use the pressure equation. So in other words, we're going to use the pressure equation. This is going to be p+rhgh. Alright. So the pbottom is going to be what? Well, that's actually really just the atmospheric pressure that we're looking for here. Right? That's at the bottom of the column of liquid. So this is just going to be your pATM or pair. And then the top part is just going to be what the top of the liquid is touching. Now remember, in a barometer, the top of the liquid is always touching a vacuum and so ptop is 0 because this is a vacuum. Alright, so that means your ptop goes away and it simplifies to ρgh. So in other words, the atmospheric pressure is just going to be your density, which is 13,600, we're going to use 9.8, and then you're going to use the h, which is going to be 0.76. Just make sure that all your units are in SI and converted. And what you get out of this is you should get 101,300 Pascals. Now if you convert this to an atmosphere, remember that one atm is equal to 101,300 Pascals. En sure that one atmosphere is exactly 101,300 Pascals.
So in other words, this is equal to exactly 1 atmosphere. Now this isn't a coincidence and I want to talk about this for a second here. Sometimes in your textbooks, you may see that this conversion of 1 atmosphere can be written in terms of Pascals, but it also might be written in terms of something else, another kind of unit, which is 760 millimeters of Hg, of mercury. Notice how 760 millimeters is 76 centimeters. So basically, what happens here is what we found is that when you have the outside air pressure of exactly one atmosphere, then if you filled your barometer with mercury, it's always going to be exactly 76 centimeters or 760 millimeters high. That's why these two things are equivalent to each other. So basically, one atmosphere is equal to 760 millimeters Hg, and it's also equal to 101,300 Pascals. All of these things here are all three common sorts of measurements or units for the pressure, the standard atmospheric pressure. Alright? So hopefully, that made sense, guys. Let me know if you have any questions.