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Math Help - newton cooling (heating actually) law problem

  1. #1
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    newton cooling (heating actually) law problem

    A thermometer reading 70 deg F is placed in an oven preheated to a constant temperature through glass window in the oven door, an observer records that the thermometer reads 110 deg F after half min and 145 deg F after one min. how hot is the oven?

    answer is 390deg Fahrenheit but i need its detail sloution next week is my seesional plz help me
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  2. #2
    MHF Contributor chisigma's Avatar
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    If we indicate with T(t) the measure of the termometer at the time t (expressed in minutes), T_{0} the measure at t=0 and T_{f} the (final) measured temperature of the owen we have...

    T=T_{0} + (T_{f} - T_{0}) \cdot (1-e^{- k\cdot t}) (1)

    In (1) there are two unknown parameters, T_{f} (that we want to find) and k (that we probably don't know). If we take into account the measured we have performed at t=\frac{1}{2} and t=1 we write...

    T(\frac{1}{2})= T_{0} + (T_{f} - T_{0}) \cdot (1-e^{- \frac{k}{2}})

    T(1)= T_{0} + (T_{f} - T_{0}) \cdot (1-e^{- k}) (2)

    In (2) you have two equations in two unknown parameters, so you can solve it and find the requested T_{f}...

    Kind regards

    \chi \sigma
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