OpenStax College Physics for AP® Courses, Chapter 14, Problem 20 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. In this question, we imagine a fire on a crude oil tanker and the question tells us how much energy is released by the burning of 1 liter of crude oil and that's 2.80 times 10 to the 7 joules and we imagine that water sprayed on it to put out this fire begins at 20.0 degrees Celsius rises up to the boiling temperature of water of 100.0 then turns into steam thereby absorbing some more energy to make that phase change happen from water to vapor and then the vapor also increases in temperature to 300.0 degrees Celsius. So how many liters of water would be needed to absorb this much energy from the burning of 1 liter of crude oil? So this is the energy that needs to be absorbed and so it's Q and Q in terms of the water is gonna be the mass of water multiplied by its specific heat times the first change in temperature from 20.0 to a 100.0 and then add to that the energy absorbed in changing phase from liquid to vapor and then add to that the energy needed to increase the temperature of that vapor from 100.0 degrees Celsius to 300.0 degrees Celsius and so we use the specific heat of steam here. So we can factor out the mass... factor from each term here and so I have rewritten it with that factored out and the question asks us for volume though so we don't really want the mass and so we have the density of water is the mass of water divided by volume and we can solve for m by multiplying both sides by V so m w is density times volume and then we make a substitution for m w with density times volume and now we have an expression containing the volume that we want to find and we can solve for it by dividing both sides by the density and this whole bracket here. So we have V equals Q divided by density times specific heat of water times the first change in temperature plus the latent heat of vaporization plus the specific heat of steam or vapor times the change in temperature number 2. So that's 2.80 times 10 to the 7 joules divided by 1000 kilograms per cubic meter—density— times 4186 joules for every kilogram per Celsius degree and that's the specific heat of water that we find in this data table here. So for water it's 4186 and for steam, it's 1520 joules per kilogram per Celsius degree. And here's the latent heat of vaporization which we can find in table [14.2]. So for water, latent heat of vaporization is 2256 times 10 to the 3 joules per kilogram so that's what's written here. So all of this works out to 0.0096722 cubic meters which we convert into liters by multiplying by 1000 liters per cubic meter and that's 9.67 liters. So it takes a lot more water for every amount of volume of crude oil. So for 1 liter of burning crude oil requires 9.67 liters of water to put it out, roughly speaking... I mean at least to absorb the energy from that burning anyhow. Now in part (b) it talks about, you know, how crude oil has a smaller density than water and what does that have to do with the difficulty in putting out the fire? Well, the water will sink below the burning oil and so you will have an oil level here and then the water will sink down below it. And so here's your water and then the fire continues to burn up top here and it's not being smothered by the water because the water's below and also the water is not absorbing any of this heat energy since it's stuck underneath the surface where the burning is happening and so the fire can continue to burn because the oil's in contact with the air still since the water has sunk below. And... yeah, here we go; difficult to put out a crude oil fire!