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course Phy 202
Measuring absolute zeroDuring 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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pressure had to rise by 3500 pascal to raise water 35cm, so the total pressure would be 103500 pascal.
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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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the two points would be (6 celsius, 100000 pascal), (22 celsius, 103500 pascal)
slope of the line would be 218.75 pascal/ degree celsius
equation of the line would be y=218.75x+98087.5, so for x=0, pressure would equal 98087.5 pascal.
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You have found the pressure when temperature is zero Celsius. That's a good result, and you have a good equation, but we are trying to find the temperature at which pressure is zero.
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We are trying to find the point where pressure is zero. So if x is the temperature, you would set y = 0 and solve for x. This would give you a tempearature between -400 and -500 Celsius.
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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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increase of 6500 pascal to a total of 106500 pascal
slope of line = 406.25 pacsal/degree celsius
equation of line y=406.25x+97562.5, so for x=0, pressure would be equal to 97562.5 pascal.
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The notes on the last question are relevant here as well.
This time you've going to get a tempearture between -200 and -250 Celsius.
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Repeat once more, using your measured height.
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measured height was 44cm
slope of line= 275 pascal/ degree celsius
equation of line y=275x+98350, so for x=0, pressure would be 98350 pascal.
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Your result here will be something a little below -300 Celsius.
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Check my notes. Take a couple of minutes and solve the equations to find the Celsius temperature at which pressure is zero, as opposed to the pressure at which Celsius temperature is zero.
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