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Math Help - Help, please

  1. #1
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    Help, please

    The Volume, V of a given mass of gas varies directly as the temperature

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    T and inversely as the pressure, P. If V= 276.0in when T= 230 degrees

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    and P= 10 lbs , what is the volume when T= 130 degrees and P = 15 lbs ?

    3
    The answer is 104.0 in Please show work so I can understand.


    Thanks
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  2. #2
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    the squares and cubes didn't come out right

    I'll repost
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  3. #3
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    In math lang:

    V \propto \frac{T}{P}

    Let V_1 = 276.0. In the transition, temperature goes from 230 to 130. So, new temperature is \frac{13}{23} of original temperature. Pressure goes from 10 to 15, and the new pressure is \frac{3}{2} of the original.

    Since V is directly proportional to T and inversely proportional to P, it will suffer a 1 - \frac{13}{23} \simeq 43\% decrease because of temperature drop and a 1 - \frac{2}{3} decrease because pressure P raises 50%. So,

    V_2 = \frac{13}{23}\frac{2}{3}V_1 = \frac{13 \times 2 \times 276 }{23 \times 3} = 104.0

    Hope it's clear,
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