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course Phy 122
9:45 pm1/26/2014
Measuring absolute zero
During the first hour of class we used the bottles as we did on the first day. This time I measured the temperature of the air in one bottle as it sat outside, then after it was brought in and allowed to sit for a time in the room. We found that its temperature rose from 6 Celsius to 22 Celsius. Water rose in the tubes of the various bottles to heights between 35 cm and 65 cm.
The pressure in the bottle was originally 1 atmosphere, which we will assume to have been 100 000 Pa. So one point on a pressure vs. temperature graph would be (6 Celsius, 100 000 Pa).
Assuming the 'low' estimate of a 35 cm water column, what would be the coordinates of the point on this graph corresponding to temperature 22 Celsius? (start by figuring out how much the pressure had to rise to support a 35 cm column of water).
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(22 Celsius, 3386 Pa)
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The pressure corresponding to 6 Celsius is 100 000 Pa.
The pressure at 22 Celsius would be greater. In fact, the 3386 Pa you calculated would be the difference in pressure due to the water column, so the pressure would be 103 386 Pa.
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Plot these two points on a graph of pressure vs. temperature. Sketch the line through these points and extend it until it reaches the point where the pressure coordinate is zero. What is the temperature coordinate at that point?
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-6038.375x + 136230.25
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This is the equation of the straight line through your two points, provided x stands for the temperature. Very good.
However this does not answer the question of where the pressure is zero.
If you correct the equation in accordance with my note on the pressure at 22 C, you will get an equation that can be used to answer this question.
Alternatively you can sketch a graph and make an estimate.
The equation would be more accurate, but either is acceptable.
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This is your estimate for the 'low' value of the height of the water column.
Repeat assuming the 'high' estimate of 65 cm for water column height.
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(22 Celsius, 6288 Pa)
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You were asked to estimate the temperature at which pressure would be zero. With a correction, this point would be useful, but more is required to answer the preceding series of questions.
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Repeat once more, using your measured height.
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(22 Celsius, 4934 Pa)
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ditto the preceding note
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You're very much on the right track, but you need a couple of revisions.
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