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Math Help - Chem with partial Derivs

  1. #1
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    Chem with partial Derivs

    What's given:
    PV=nRT P is pressure, T temperature, V volume, n moles, r is ideal gas constant (.08206)

    Assume that we have ten moles of gas in a balloon type bladder. Initially we have a volume of 224.15 liters at Standard Temperature and Pressure. (T=273.15, P=1atm) As time goes on gas is heated. The following equation expresses the temperature T of the gas as a function of time elapsed, t since the beginning of the experiment:
    T= 323.15 - (50/(t+1))

    The bladder begins to expand over time as a function also of the strength S of its material with the following formula describing how the volume V of the gas which can occupy the bladder changes as a function of the number of minutes and the material strength S

    V= 4-2e^(-3ts)

    a) Describe, by means of an appropriate partial derivative, how the pressure of the gas in the bladder changes as a function of time.

    b) Describe by means of an appropriate partial derivative how the pressure of the gas in the bladder changes as a function of the strength of the bladder.



    ok... so I've gotten kind of lost with this problem. My first thoughts were to plug formula V & T, and number N(10 moles) into the PV=nRT formula then derive with respect to T, then do the same with respect to S. Is this on the right track?
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  2. #2
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    If P=nR\frac{323.15-\frac{50}{t+1}}{4-2 e^{-3ts}} then what is \frac{\partial P}{\partial t} and \frac{\partial P}{\partial s}?
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