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Mathematics
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. Show that the rule Vi/Vf = Ti/Tf says that if we have a constant amount of gas and keep the air pressures from changing, that cooling such a mass of air will cause it to shrink.
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Well if you're cooling, then you know that the final temperature is lower than the initial temperature. So one possibility is you halved the temperature. So you could plug this in and see what you get as the relationship between the two volumes is \[\Large T_f=\frac{1}{2}T_i\]
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