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Math Help - Differentials

  1. #1
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    Differentials

    Question: The pressure, volume and temp. of an ideal gas are related by the equation: PV=nRT. where P is menasured in KPA(kilo pascals), V in liters, and T in kelvins. Use differentials to find the approximate change in the pressure if the volume increases from 12L to 12.3L and the temperature decreses from 310K to 305K. Any idea how to do this?
    Thank you
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  2. #2
    MHF Contributor Calculus26's Avatar
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    P = nRT/V

    dP = dP/dT dT + dP/dV dV where dP/dT and dP/dV are actually partial derivatives

    dP = (nR/V)dT - (nRT/V^2)dV

    Fill in the data and you're done
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    thank you
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by fearless901 View Post
    Question: The pressure, volume and temp. of an ideal gas are related by the equation: PV=nRT. where P is menasured in KPA(kilo pascals), V in liters, and T in kelvins. Use differentials to find the approximate change in the pressure if the volume increases from 12L to 12.3L and the temperature decreses from 310K to 305K. Any idea how to do this?
    Thank you
    P=\frac{nRT}{V}

    dP=\frac{\partial P}{\partial V}dV+\frac{\partial P}{\partial T}dT

    dP=-\frac{nRT}{V^2}dV+\frac{nT}{V}dT

    from here just plug in the values and you are done.


    EDIT: WOW I was really late hehe
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