woozy
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Obviously I have a misconception somewhere. But where?
This are my conceptions; one (or more) of them must be wrong:
[edit: I thought it was clear I meant which conceptions were *fundamentally* flawed "false hypothesis" that lead to the false conclusion and not which conceptions contain errors or are wrong because they are conclusions drawn from false hypothesis. Conceptions containing errors that are not fundamental to the argument bear correction but don't yield false conclusions.]
1. A specific gravity reading is ratio between the density of liquid compared to the density of water (calibrated for a specific temp. but lets not bog ourselves down). Thus, for example, if a solution has an s.g. of 1.046 that means the solution is 1.046 times as dense as water.
2. Density is mass/volume. Weight is measure of gravity on a mass and in this case can be considered synonamous with mass so density is (on earth at sea level) also a measurement of weight/volume.
[edit: "can be considered synonamous" has received a lot of criticism. Mass and weight, are of course, utterly different concepts. I should have worded this more carefully. My intention was not to imply they were the same thing but that, for the purpose of this argument density, although defined as mass to volume, can be used to also express weight to volume. This doesn't fundamentally affect the argument.]
3. Thus: a gallon of something with an s.g. of 1.046 will be 1.046 times as heavy as a gallon of water.
4. A gallon of water weighs 8 lbs so a gallon of something with an s.g of 1.046 will weigh 8.368 lbs.
[This is incorrect. "A pints a pound the world around" apparently is *never* true. A gallon of water is 8.33 lbs. It doesn't affect the argument but it does lead to incorrect values.]
5. Soluable means disolves in water thus adding it to water will not increase the volume.
[*THIS* is fundamentally incorrect and gives rise directly to the incorrect conclusion.]
6. Sugar is soluable in water thus added a pound of sugar to a gallon of water will result is one gallon of solution.
[Since this is based on a false hypothesis this is, of course, incorrect.]
7. Sugar has a diastatic power of 46 PPG which means adding 1 lb of sugar to one gallon of water will yield a solution with a s.g. of 1.046
[This has two errors, neither fundamental to the argument. i) "diastic power" simply was not the term I wanted. "diastatic power" is a measure of enzyme activity and sugar, of course, has none. I incorrectly used it to mean the degree to which it effects gravity. ii) One doesn't add sugar to a gallon of water; one adds sugar and enough water to make a gallon of solution.]
8. Thus 1 lb of sugar added to a gallon of water will be one gallon in volume and thus weigh 8.368 lbs.
[This is based on the false hypothesis #5 so as a result is false]
9. Adding a lb of sugar to a gallon of water causes no chemical of physical reaction that will result in any loss of mass or weight.
10. 1 lb of sugar weighs a lb. A gallon of water weighs 8 lbs so mixing the two results in a solution weighing 9 lbs.
[Well, 9.33 lbs...]
11. 9 lbs is a different weight than 8.368 lbs
Which of my conceptions is [fundamentally]wrong?
[#5 ]
This are my conceptions; one (or more) of them must be wrong:
[edit: I thought it was clear I meant which conceptions were *fundamentally* flawed "false hypothesis" that lead to the false conclusion and not which conceptions contain errors or are wrong because they are conclusions drawn from false hypothesis. Conceptions containing errors that are not fundamental to the argument bear correction but don't yield false conclusions.]
1. A specific gravity reading is ratio between the density of liquid compared to the density of water (calibrated for a specific temp. but lets not bog ourselves down). Thus, for example, if a solution has an s.g. of 1.046 that means the solution is 1.046 times as dense as water.
2. Density is mass/volume. Weight is measure of gravity on a mass and in this case can be considered synonamous with mass so density is (on earth at sea level) also a measurement of weight/volume.
[edit: "can be considered synonamous" has received a lot of criticism. Mass and weight, are of course, utterly different concepts. I should have worded this more carefully. My intention was not to imply they were the same thing but that, for the purpose of this argument density, although defined as mass to volume, can be used to also express weight to volume. This doesn't fundamentally affect the argument.]
3. Thus: a gallon of something with an s.g. of 1.046 will be 1.046 times as heavy as a gallon of water.
4. A gallon of water weighs 8 lbs so a gallon of something with an s.g of 1.046 will weigh 8.368 lbs.
[This is incorrect. "A pints a pound the world around" apparently is *never* true. A gallon of water is 8.33 lbs. It doesn't affect the argument but it does lead to incorrect values.]
5. Soluable means disolves in water thus adding it to water will not increase the volume.
[*THIS* is fundamentally incorrect and gives rise directly to the incorrect conclusion.]
6. Sugar is soluable in water thus added a pound of sugar to a gallon of water will result is one gallon of solution.
[Since this is based on a false hypothesis this is, of course, incorrect.]
7. Sugar has a diastatic power of 46 PPG which means adding 1 lb of sugar to one gallon of water will yield a solution with a s.g. of 1.046
[This has two errors, neither fundamental to the argument. i) "diastic power" simply was not the term I wanted. "diastatic power" is a measure of enzyme activity and sugar, of course, has none. I incorrectly used it to mean the degree to which it effects gravity. ii) One doesn't add sugar to a gallon of water; one adds sugar and enough water to make a gallon of solution.]
8. Thus 1 lb of sugar added to a gallon of water will be one gallon in volume and thus weigh 8.368 lbs.
[This is based on the false hypothesis #5 so as a result is false]
9. Adding a lb of sugar to a gallon of water causes no chemical of physical reaction that will result in any loss of mass or weight.
10. 1 lb of sugar weighs a lb. A gallon of water weighs 8 lbs so mixing the two results in a solution weighing 9 lbs.
[Well, 9.33 lbs...]
11. 9 lbs is a different weight than 8.368 lbs
Which of my conceptions is [fundamentally]wrong?
[#5 ]