Homework4_prblms

# Homework4_prblms - C is increasing exponentially in time...

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MAE 118A Homework 4 Quiz on this material will be held Wednesday 2 December 2009. 1. Suppose that for t<0 the carbon emission rate is a constant value, Q C1 . At t=0 the emission rate then changes suddenly to a different value, Q C2 . If the net C uptake timescale, t net , is constant, find the atmospheric carbon mass for all times. 2. In general Q C (t) is not constant and is, in general, a function of time, i.e. Qc=Qc(t). The carbon balance equation in this case is an inhomogenous linear ODE with constant coefficients. Show that in this case the general solution for the atmospheric carbon mass is given as 3. Suppose that Q
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Unformatted text preview: C is increasing exponentially in time such that Q C =Q C0 exp(rt). Here Q C0 =Q C (t=0). Find the evolution of the atmospheric carbon mass, Mc(t), and the evolution of the infra‐red transmission coefficient, , in this case. 4. Suppose Q C =Q C0 =const for t<0 and then it decreases exponentially in time for t>0 such that Q C =Q C0 exp(‐rt). Find the evolution of the atmospheric carbon mass, Mc(t), and the evolution of the infra‐red transmission coefficient, , in this case. ! M C ( t ) = ! M C (0) + e " t / # eff e \$ t / eff Q C ( \$ t ) d \$ t t %...
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