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I'm learning about thermodynamics for the first time and have reached the chapter regarding expansion of materials due to change in temperature but an example in the book isn't adding up with the information they've provided already.

The example states that the mass of gasoline in a fuel tank in summer is less than in winter because it's expanded but that doesn't make sense to me. Like, if the tank had 10 litres of fuel in it, it would expand in the summer due to the higher temperature and therefore appear on the gauge as if you have more fuel than you actually do. In winter however, the gasoline hasn't expanded and so it appears like you have less fuel but the actual mass of gasoline hasn't changed, it's still 10 litres. The density would've changed because the volume has changed but the mass would still be the same, right?

Could someone explain what I'm missing?

Thanks

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    $\begingroup$ Liters are not kilograms… $\endgroup$
    – Jon Custer
    Commented Mar 20, 2023 at 21:49
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    $\begingroup$ Note - that gasoline is stored in underground tanks at the gas station. The temperature in those tanks does not vary nearly as much as ambient temperatures. $\endgroup$ Commented Mar 20, 2023 at 22:46
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    $\begingroup$ The quoted text refers to filled tanks; a filled tank in summer does have less mass of gasoline than a filled tank in winter... $\endgroup$
    – DJohnM
    Commented Mar 21, 2023 at 20:59

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You are correct, and the book is wrong.

The mass of the fuel does not change at all. If the temperature increases, the density will decrease and the volume will go up. The reverse happens when the temperature drops, but at no time does the mass change.

The mass is caused by the number of molecules of fuel that are put in the tank. That number does not change. As the temperature goes up, the increased speed of those molecules keeps them further apart; hence the volume increases.

Perhaps the confusion comes from the fact that, in winter, that same mass takes up a smaller volume and hence the gauge (which measures volume), indicates a smaller amount of fuel.

EDIT

On re-reading the question after Chemomechanics comment, I agree the book does not say the mass changes; what changes is the mass of the fuel left when the gauge reads empty.

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  • $\begingroup$ And the real problem is that in many areas ethanol is added in winter to reduce smog, so you get worse mileage in the winter. This effect far outweighs any density changes. $\endgroup$
    – Jon Custer
    Commented Mar 20, 2023 at 23:18
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    $\begingroup$ "You are correct, and the book is wrong." The source never claims a certain mass changes, as you seem to think it does. It states that a warmer mass corresponding to a certain volume (the liquid height threshold that triggers the "empty" light) is less than a colder mass corresponding to the same volume. I don't see the problem with that. $\endgroup$ Commented Mar 21, 2023 at 5:40

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