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Homework Help: Related rates volume problem

  1. Nov 4, 2009 #1
    1. The problem statement, all variables and given/known data

    When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.14=C, where C is a constant. Suppose that at a certain instant the volume is 600 cm^3 and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what rate is the volume increasing at this instant?

    2. Relevant equations
    we want dV/dt when V=600 and P=80

    3. The attempt at a solution
    V=(1.4 root)(C/P)
    then i plugged in P=80 and C=620157 to get an answer of 192.5 cm^3/min which was wrong.

    Can anyone show we where I went wrong and how to get the proper solution?
  2. jcsd
  3. Nov 4, 2009 #2


    Staff: Mentor

    Error in next line. The constant is 1.14, not 1.4. Also, there are square roots, cube roots, fourth roots, and so on, but not 1.4 or 1.14 roots.
    PV1.14 = C, so V1.14 = C/P, so V = (C/P)1/1.14
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