Hot Gasoline

In St. Louis local news, there’s a brouhaha over ‘hot gas’ — how the gasoline companies have conspired to gouge us at the pump because they don’t take into account the current temperature of the gasoline being pumped.

Stories like this come up at lot, at least in St. Louis, thanks to the ‘investigative reporting’ (read: badly-informed muckraking) of NBC 5’s I-Team and Fox 2’s You Paid For It. These stories are always a mixture of baseless accusations, impassioned posturing, and men in suits trying to get back to their jobs.

“We tried to talk to alderman Joe Smith by showing up to a scheduled board meeting with a camera crew and lights and shoving a microphone in his face, instead of scheduling a meeting with him and agreeing on a time to interview him. He refused to talk to us and threw us out of the meeting. What is he trying to hide?”

But sometimes the stories are so off-base that they make the scientist in me cringe, and the ‘hot gas’ story is one of those. This has been going around on talk radio for a while, and I hear people in the gas stations bitching about it (because they heard about it on the radio).

Fill ‘Er Up

The crux of this controversy over hot gasoline is that gasoline, like most other liquids, expands when it is heated. (Even water does this, although weird stuff happens to water when it cools, but that’s another story.) So when you pump 10 gallons of hot gasoline into your car’s gas tank, it will be less than 10 gallons when it cools off.

The real problem here is that we measure gasoline in gallons (a volume), when what we’re really interested in is joules (a measure of energy). It’s sort of how we weigh ourselves in pounds (a force), when what we’re really interested in is kilograms (a mass). We’ll encounter a similar controversy, I’m sure, when we finally populate the moon. Weight-conscious people will take a vacation to the moon, step on a scale and say “Hey! I only weigh 33 pounds here, but on Earth I weighed 200 pounds! Why does the Earth government want me to think I’m heavier than I really am?”

(I’m just kidding, of course. When we finally populate the moon, the scales will be calibrated to show what you would way in Earth pounds, even though that number will have essentially no meaning.)

If we measured gasoline in MJ (megajoules), we’d just say “fill ‘er up with a thousand”, not caring how many gallons that is, and we’d use about 5 MJ per mile, and there wouldn’t be a problem; we’d join hands and sing songs about how happy we are that our units finally make sense.

But we don’t do that, so.

How much, exactly, are we talking about?

Where’s My Nerd Hat?

The first thing we need to decide is what the ‘standard temperature’ is for a gallon of gasoline. Really, we need a standard temperature and pressure, but we’ll just ignore pressure for now. (Coming next week: Why you pay more for gasoline in the mountains!)

Since a good ‘room temperature’ is 75°F, we’ll use that as our standard temperature. When we pump gas, we expect that the gas will be at 75°F, and if it’s hotter, then by God, we’re getting ripped off!

In order to calculate the change in volume of a liquid, we use the general equation:

ΔV = β × V₀ × ΔT

This formula says that the change in volume (ΔV) is equal to the initial volume (V₀), multiplied by the change in temperature (ΔT), multiplied by the coefficient of volume expansion (β). Note that all temperatures are specified in Celsius, because that’s the nerd way of talking about temperatures.

For gasoline, β is approximately 9.50×10^-4. See here and here, and convert the number into proper nerd format.

Let’s say you pump 10 gallons of gas on a hot summer day, when the gasoline is 92°F. The gasoline, which is stored in underground tanks, probably doesn’t get this hot, but let’s say it does for the sake of argument. Later, you park your car in your garage and the gasoline cools down to 75°F. This means that the nerd temperature of the gas has changed from 33.3°C to 23.9°C, so ΔT is -9.4°C.

So, we’ve got the following:

β = 9.50×10^-4
V₀ = 10
ΔT = -9.4

I’m leaving off the units here because they balance (trust me), and I’m not bothering to convert our 10 gallons into nerd units because I’d just convert it back afterward anyway. So now we can say:

ΔV = 9.50×10^-4 × 10 × -9.4
ΔV = -0.0893

In other words, after your gasoline cools down, you will have 0.0893 fewer gallons than when you started. Since we started with 10 gallons of gasoline, we now have 9.9107 gallons.

What does this mean in terms of cost? It means that you’ve paid for 0.0893 gallons of gasoline that you weren’t given. At the current local price of $2.959 per gallon, we’re paying 26.4¢ extra for our 10 gallons of gas.

If we consume 10 gallons of gas a week, we’d be paying $13.74 extra every year for gas we never got. We could buy, like, a pizza with that kind of cash. The gasoline companies are denying us one pizza every year!

But Wait, There’s More

Hang on, though, it’s not summertime year-round. What about in the winter, where the temperature drops to a balmy 20°F? Well, then our ΔT is 30.5°C (23.9°C - -6.6°C). We pump the same 10 gallons of gas, and of course β stays the same, so we have:

β = 9.50×10^-4
V₀ = 10
ΔT = 30.5

From the original equation:

ΔV = 9.50×10^-4 × 10 × 30.5
ΔV = 2.8975

Yikes! On really cold days, we’re pulling away from the pump with almost three gallons of gas we didn’t pay for! At the same $2.959 per gallon, that would cost $8.57 or so. If you fill up just twice in the wintertime, you can make back all of the extra money you spent on gas in the summertime, and maybe a little more.

In Summary

Although I’m sure that American corporations will gladly screw you in any way possible for profit, this whole thing is really the problem it’s being made out to be. In the summer days, you effectively pay about 2¢ more per gallon than you should. In the winter, you pay about 86¢ less than you should.

These numbers really are higher than they should be, because the gasoline is stored in underground containers which keeps it warm in the winter and cool in the summer. We’re really probably talking about a cent or so extra in the summer and about 20¢ less in the winter.

What people ought to be more angry about is that when a refinery has to temporarily close, even for just a few days, gas prices across the nation spike, even at stations that don’t depend on that refinery.

That is American corporations sodomizing at their best.