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 ?

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

Thanks

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

I'll repost

3. In math lang:

$\displaystyle V \propto \frac{T}{P}$

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

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

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

Hope it's clear,