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Queen Nefertari Solution

Part A


Overall balance on the CO2 in the tomb.

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Part B


Laplace transform and the transfer functions

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Input function is a pulse of finite width which is represented by a step up followed by a step down only delayed by t1.

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Final laplace transform

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Final time function

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Where does the maximum occur? Well (and this requires proof not given) it is clear that the first part of the curve reaches its maximum at time t1 since it is a monotonically increasing function. Since the second part of the curve is a monotonically decreasing function this has its maximum also at t1, therefore the overall function max occurs at t1.

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Part C


Do two balances one on CO2 again and now one on the people in the tomb as the other state variable.

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The matrices follow directly after the linearization of the second equation to account for both the flow and concentration changing. Note that CI is constant.

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The rest is then just to plug through the (sI-A)-1 and multiply by the B and gamma matrices.




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