We’re going to calculate

the volume of water vapor superheated steam from the ideal gas law and then we’re going to compare

it to volumes that we obtain from the steam table. So, of course, the volume of steam tables are measured values and the idea is how much

air do we make by assuming ideal gas law. We’re going to do this,

a couple conditions. Same temperature, 500 degrees C but relatively low pressure, point five megapascals,

it’s five bar pressure or high pressure 17 megapascals pressure. So let’s look at the ideal gas law and what we’re solving for is volume. And we’re solving for specific volume. So the ideal gas law looks like this. The gas constant, of course, is a function of

which units we’re going to use. I just looked up a gas

constant in the table and then I’ll just do

some units conversion. So this is in terms of megapascals but cubic centimeters, moles, and kelvin. Temperature 500 degrees C, but of course we have to

use absolute temperature. So we add 273 to convert that to kelvin and then the pressure 0.5 megapascals. So I’ll calculate the end. And now I wanna convert this volume rewrite this and write down

some conversion factors. So I’ve written a conversion

from centimeters to meters or cubic centimeters to cubic meters. And then one mole for water is 18 grams and since I want the answer in kilograms, 10 to the 3rd grams is one kilogram. So I can multiply this out and so here’s the value ideal gas law 0.714 cubic meters per kilogram. The measured value from the steam tables 0.7109 cubic meters per kilogram. Really very close if I

subtract these values and then calculate what

percentage error this is. Let me stop and do that. So I took the difference,

divided by the measured value, multiplied by 10 squared

to make a percent. So notice, error we’re making

is less than half percent if we use the ideal gas law. Let’s do the same calculation

at the higher pressure. So here’s the value I calculate. Same type calculation and again let me do the units conversion. So value I calculate, of course it’s smaller because

we’re at higher pressure but now if I compare

this to the value from the steam tables which is 0.0482

cubic meters per kilogram. This is from the steam tables and his is ideal gas. So pretty big difference. Factor of two. So clearly at this high pressure, this is 170 bar pressure, idea gas law is not a

good model for water vapor and the reason is that as we

go to these high pressures for the ideal gas law, we’re assuming molecules

don’t have any volume, don’t occupy any space. But of course, as we start

getting molecules of water close together there’s repulsion, they do occupy space and thus you see that the

actual volume is much larger because we can’t assume

at these conditions that the molecules occupy no space.

Thanks stan lee.

This video describes specific volume, which is very different from volume which was the word chosen for the title. Got my hopes up this was almost exactly what I'm looking for.