[RESOLVED] modelling problem

[hani1987]

hi

im stuck on an additional homework problem, any ideas on how to solve appreciated

A sphere of ice i melting so its volume decreases whilst it maintains the same shape (but not size).

(a) Use volume balancing to derive differential equations describing the rate of change of the radius of the sphere , r, if it is melting:

i) with a constant rate of volume loss;
ii) at a rate of volume loss proportional to the surface area of the sphere;
iii) at a rate of volume loss proportional to the volume itself.

-constants of proportionality are k1, k2, and k3

-solve each of the equations to find an expression for r as a function of time t, assuming that the initial radius of the sphere is ro.

-ro = 2x10^-3, k1= 10^-6 m^3 s^-1
k2 and k3 should be chosen to make the initial rate of melting the same in all 3 cases.

thanks,

Donna