The deepest point in the ocean is 11 km below sea level, deeper than Mt. Everest is tall. What is the pressure in atmospheres at this depth?

Video transcript

Hey, everyone in this problem, we're told to suppose that a volcanic eruption at the bed of the ocean creates a new deepest point with the depth of 12.5 kilometers below the surface of the ocean. We're asked to determine the pressure at the deepest point. We're told to take the density of ocean water row to be kg per meter cube. We have four answer choices all in pascal option, a 1.01 times 10 to the exponent five. Option B 1.26 times 10 to the exponent eight. Option C 1.24 times 10 to the exponent 13. And option D 1.39 sorry 1.29 times 10 to the exponent seven. Put the pressure on a particular depth. Let's recall that the pressure P at depth age is gonna be equal to P on the pressure at the surface. The last row multiplied by G multiplied by H where row is the density G is the acceleration due to gravity and H is the depth. No, we have our pressure because we know the pressure at the surface of the ocean we're given the density, we know the acceleration due to gravity, we're given the depth. So this is a simple problem where we just need to substitute in the values we were given now that we have the correct equation and solve. So we get that the pressure P is going to be equal to. Yeah, P not the pressure of the surface of the ocean. This is a um constant that you can look up in a table in your textbook or that your professor provided this is gonna be 1. times 10 to the exponent five plus the density kilograms per meter cubed multiplied by the acceleration due to gravity 9.8 m per second squared multiplied by the depth which is 12.5 kilometer. And we want to write this in our standard unit of meters. So to go from kilometers to meters, we multiply by 1000. So we have 12.5 times 10 to the exponent three. All right. So we have meters multiplied by meters in the numerator meters cubed in the denominator. So that's gonna leave us with just meter in the denominator. So we have a kilogram per meter second square which recall is equivalent to a pass scale. And so what we get is that the pressure of P at this particular depth gonna be equal to 1.01325 times 10 to the exponent five fast scales plus, simplifying all this stuff in the second term, 1.26175 times 10 to the exponent eight pascals. And if we simplify this, we get that our pressure that we're looking for is 1. 276, 325 times 10 to the exponent. OK. So the answer choices are rounded to two decimal places. So we're gonna go ahead round our answer to two decimal places. And we can see that it corresponds with answer choice B 1. times 10 to the exponent eight. Pascal. Thanks everyone for watching. I hope this video helped. I'll see you in the next one.