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Thread: Chemistry and Derivatives!

  1. #1
    Feb 2010

    Chemistry and Derivatives!

    I have a calculus project due tomorrow and help would be greatly appreciated!
    The problem: Imagine that .00158 moles of CO2 is contained in a closed pipette whose volume is decreasing at the rate of .001L/sec, while the pressure is increasing at the rate of 1/2 atm/sec and the moles are increasing at a rate of .0001881moles/sec. How fast is temperature changing when pressure is 5.2atm, volume is .0055L Moles increase at a rate of .0001881 moles per second.

    The equation we wish to take the derivative of is PV=nRT, solving for the rate of change of temperature over time. (dT/dt).

    To make it more clear:
    dP/dt= .5atm/sec P=5.2 atm
    dV/dt= -.001 L/sec V= .0055L
    dT/dt=? T= 220 K
    dn/dt=.0001881 n=.00158

    Thanks in advance, I have tried to solve this problem for the past week and cannot get a reasonable answer for dT/dt.
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  2. #2
    Newbie blackcompe's Avatar
    Feb 2010
    I solved the ideal gas law for T: T = PV/nR. Therefore, T', which is the rate of change of the temperature with respect to time is: ((PV)'(nR) - (PV)(nR)') / (nR)^2, by way of the product rule.

    T' = ((PV)'(nR) - (PV)(nR)') / (nR)^2
    = ((P'V + PV')(nR) - (PV)(n'R + nR')) / (nR)^2

    Since you've got P', V', n', and you know derivative of a constant, R, is 0, you can solve for T'. I got approximately -45 K/sec for T'. Good luck.
    Last edited by blackcompe; Feb 9th 2010 at 05:56 PM.
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