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Thermodynamics |
Thermodynamics |
volume-temperature (constant pressure)What happens to the volume of a gas when its temperature changes? Let's try another kitchen experiment.
Bread is made from wheat flour, water, yeast, and a bit of sugar. Yeast are tiny microorganisms. They are quite possibly the very first domesticated animals and, much like dogs and horses, yeast have been bred for different purposes. Just as we have guard dogs, lap dogs, and hunting dog; draft horses, race horses, and war horses; we also have brewer's yeast, champagne yeast, and bread yeast. Bread yeast have been selectively bred to eat sugar and burp carbon dioxide (CO 2 ). When wheat flour and water are mixed together and kneaded, the protein molecules are mashed and stretched until they line up neatly to form a substance called gluten that, like chewing gum, is both elastic and plastic. Let this special matrix sit and the the CO 2 vented from the yeast get trapped in thousands of tiny resilient, stretchy pockets. As this process continues these tiny pockets expand, which causes the volume of the dough to expand or rise in a process called proofing . We now have a fluffy gummy blob ready for the oven. While there the dough expands again, but his time it's not due to the action of microorganisms (they all die around the boiling point of water). This time it's the heat, or rather the temperature. The temperature inside a bread oven is roughly 50% greater than the temperature outside. And similarly, the baked bread that comes out of a bread oven is also roughly 50% greater than the room temperature dough that goes in. This domestic example illustrates quite nicely a fundamental property of gases. The volume of a gas is directly proportional to its temperature when pressure is constant. Symbolically . V ? T While no doubt known and understood informally by billions of bakers since the dawn of civilization, the precise mathematical relationship was first discovered by the French physicist Guillaume Amontons (1663-1705) in 1699. The experiment was repeated much later by Jacques Alexander Cèsare Charles (1746-1823) in 1787 and much, much later by Joseph Louis Gay-Lussac (1778-1850) in 1802. Charles did not publish his findings, but Gay-Lussac did. It is most frequently called Charles' law in the British sphere of influence and Gay-Lussac's law in the French, but never Amonton's law. An isobaric process is one that takes place without any change in pressure. Let's recall what it means when two quantities are directly proportional like volume and temperature. Heat up a gas and it's volume will expand. Cool it down and it's volume will contract. The two quantities change in the same direction. More specifically, and increase in one results in a proportional increase in the other and a decrease in one results in a proportional decrease in the other. For example .
There's a symmetry at work here somewhere. A symmetry is a change in one quantity that leaves another, more fundamental quantity unchanged. It's something like multiplying both the numerator and denominator of a fraction by the same thing.
No wait, it's exactly like that. The only way two quantities can change in direct proportion is if their ratio remains constant. Thus .
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