1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    dP/dt=-10
    we want dV/dt when V=600 and P=80

    3. The attempt at a solution
    V=(1.4 root)(C/P)
    80(600)^1.4=C
    C=620157
    dV/dt=1/1.4(C/P)^-0.4((cp'-pc')/p^2)dP/dt
    =1/1.4(C/P)^-0.4((c10-0)/p^2)(-10)
    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

    Mark44

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Related rates volume problem
  1. Volume; Related Rates (Replies: 4)

Loading...