Torricelli, who invented the barometer, used mercury in its construction because mercury has a very high density, which makes it possible to make a more compact barometer than one based on a less dense fluid. Calculate the density of mercury using the observation that the column of mercury is 760 mm high when the atmospheric pressure is 1.01 * 105 Pa. Assume the tube containing the mercury is a cylinder with a constant cross-sectional area.

Video transcript

Hey everyone in this example, we need to determine the density of glycerol in grams per mil leader. If we have 1.50 m of a column of glycerol exerting a pressure of 0.1 83 A t. M's. So because they want our final answer to be expressed in units of grams per meal leader, we want to convert our pressure into units of paschal's and then from units of paschal's into units of kilograms divided by meters times seconds squared. So we're gonna take that given pressure value 0. 83 80 M. And go through that conversion. So in our denominator to go from a T. M. To pascal, we should recall that for 1 80 M, we have one point oh one times 10 to the fifth power pascal's. And so now we're able to cancel out our units of a T. M. S. And now we're going to have our answer here for pressure in pascal's. This gives us a value of 1000 or 18, pascal's as our pressure. And we're going to recall that one Pascoal is equal to the other pressure unit of one kg divided by meters times seconds squared. So we can re interpret this as 18, kg divided by meters times seconds squared as our new pressure. Now recognize that in this question were given the term column of glycerol. And so this should tell us that we're going to be using our pressure head formula which is represented by this capital p here. So the pressure head of a liquid we should recall is equal to the density of our liquid multiplied by gravity and then multiplied by the height of our liquid. And we want to solve for density our D value here which is given in the problem. So we would reinterpret this formula to have density equal to our pressure divided by our gravity of our or the gravity times height. And so what we would have is that our density is going to equal in our numerator. We're going to plug in that pressure 18,483 kg divided by meters times seconds squared. And then in our denominator we're going to plug in first. Our gravity which we should recall is a value of 9. m per second squared. And then also multiplied by our given height as in the problem 1.50 m. And so canceling out our units. We would be able to get rid of our units of second squared, leaving us with all of our other units. And we're going to get a value for this quotient equal to 1, where we have units of kg in the numerator. And then when we multiply all of the meters in our denominator we would have meters cubic meters and this is our units for density so far. But again the question wants us to give the density and grams for middle leaders. So we're gonna have to keep making conversions. So we want to go ahead and go from kilograms to grams and just for purpose of room. I'm just going to carry this down below here. Oops, sorry about this. So we have our density value equal below here and we're gonna just continue on to convert from kilograms to grams by recalling that are prefix kilo, tells us that we have 10 to the third power grams. So now we can cancel out kilograms. We're left with grams per cubic meters. So we want to go ahead and cancel out those meter units or those cubic meter units. So we would recall that we have for one cubic meter 10 to the sixth power milliliters, which is what we want for our final unit. So now we can go ahead and get rid of cubic meters, leaving us with grams per mil leader for our proper density units. And so this is going to give us a final value. When we take this product in our calculator, we're going to get 1.26 g per milliliter as our density of our glycerol. And so this is going to be the final answer to complete this example. So I hope that everything are viewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video