Avg Coefficient of Volumetric Expansion

[k0b3]

I really don't know what the problem is with these questions but I seem to be getting within 10% of the correct answer. Here is an example question:

The density of gasoline is 730 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 10-4 / C°. Assume 1.00 gal of gasoline occupies 0.00380 m3 How many extra kilograms of gasoline would you get if you bought 15.0 gal of gasoline at 0°C rather than at 22.0°C from a pump that is not temperature compensated?

Converting to KG then using the volumetric expansion equation (change if V = V times beta times delta T), I got the answer .879. I checked with friends and what not and they all seem to be getting the same answer but it says it's wrong and within 10% of the value. I get the same incorrect response for other very similar problems. Anyone know what is wrong?

 

[alphysicist]

Hi k0b3,

I really don't know what the problem is with these questions but I seem to be getting within 10% of the correct answer. Here is an example question:

The density of gasoline is 730 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 10-4 / C°. Assume 1.00 gal of gasoline occupies 0.00380 m3 How many extra kilograms of gasoline would you get if you bought 15.0 gal of gasoline at 0°C rather than at 22.0°C from a pump that is not temperature compensated?

Converting to KG then using the volumetric expansion equation (change if V = V times beta times delta T), I got the answer .879. I checked with friends and what not and they all seem to be getting the same answer but it says it's wrong and within 10% of the value. I get the same incorrect response for other very similar problems. Anyone know what is wrong?

It's difficult to follow what you did since there are no intermediate results in your post, but it seems to me that you found that there were more kg of gasoline in the tank at the hotter temperature. Can you see that that can't be true? As it expands, a specified volume of gasoline will weigh less and have less mass.

To solve this, think about what quantity is actually changing in this problem (besides the mass change that you are asked for). If you don't get the right answer, please post the numbers you got and the values you multiplied together to get them, for both temperatures.

 

[StarmanJV]

you base numbers are good//they correspond to a density of 0.730 g/cc. at 0C. therefore a cc will expand to 1.022cc at 22C...or a density of 0.714. The heat value of a hydrocarbon is around 11 kcal per gram so you wouild lose about 2% if in fact this were the case. However except in very unusual circumstances, like fresh delivery from a warm truck, the temperature of gas delivered at the pump stays remarkably close to underground temperatures down 5 or 6 feet.

 

[climer97007]

Okay, let's extend this one step further.

I am trying to figure out how much total expansion I would get from liquid gasoline at 21.1C (70F) after it is heated up to 204.4C (400F).

The equation you are using only seems to hold-up for temperatures where gas is a liquid. After I have turned the gasoline into a vapor, how do I compute it's volumetric expansion with temperature? What formula would I use?

In other words, if I have 1 cubic foot of vaporsied gasoline at 100C, how many cubic feet do I have at 200C?

Thanks,
Gene

 

[climer97007]

I am trying to figure out how much total expansion I would get from liquid gasoline at 21.1C (70F) after it is heated up to 204.4C (400F).

The gas law equations only seem to hold-up where gasoline stays as a liquid, or has already been converted to a vapor. Ican find nothing to help explain or predict what happens in the transition phase from liquid to a gaseous form.

What I am working on is figuring out what the liquid-to-gas expansion ratio is for gasoline and its constituent substances. One cubic foot of liquid gasoline equals how many cubic feet of gaseous gasoline? What about Toluene? Benzene? Xylene? Etc... I figure the ratios are 100's to 1. But, what are they? Anyone have a table of ratios for various liquids? Thanks, Gene