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Math Help - Derivative problem

  1. #1
    s3a
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    Derivative problem

    First of all, let me say this question sounds like a chemistry question but it's a problem in my Calculus 1 book.

    Question:

    Boyle's Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant: PV = C.

    (a) Find the rate of change of volume with respect to pressure.

    (b) A sample of gas is in a container at low pressure and is steadily compressed at constant temperature for 10 minutes. Is the volume decreasing more rapidly at the beginning or the end of the 10 minutes? Explain.


    Answer: dV/dP = -C/P^2

    I am stuck on (a).

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    p_1V_1=p_2V_2\rightarrow \frac {V_1}{V_2}=\frac {p_2}{p_1} Think about (b).
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  3. #3
    s3a
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    You're supposed to use a derivative way to solve this and I don't see how (p1)(V1) = (p2)(V2) would help there. I'm still trying to do the problem and I've almost got the answer! I just don't see why there is a negative sign.

    My work is attached as #53 (the last problem) (written in blue).

    (b) is obvious to me without even doing the math.
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  4. #4
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    Quote Originally Posted by s3a View Post
    First of all, let me say this question sounds like a chemistry question but it's a problem in my Calculus 1 book.

    Question:

    Boyle's Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant: PV = C.

    (a) Find the rate of change of volume with respect to pressure.

    (b) A sample of gas is in a container at low pressure and is steadily compressed at constant temperature for 10 minutes. Is the volume decreasing more rapidly at the beginning or the end of the 10 minutes? Explain.

    Answer: dV/dP = -C/P^2

    I am stuck on (a).

    Any help would be greatly appreciated!
    Thanks in advance!
    V = \frac{C}{P} = C P^{-1}. NOw do the differentiation.
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