A gas may be approximated to have a temperature$-$independent heat capacity at constant volume of $\frac{?}{\text{b}\text{a}\text{r}}(C{)}_V=\frac{5}{2}R.$ That gas, acting as an ideal gas, is trapped in a piston system as depicted in the right$-$hand drawing of Figure $2\mathrm{.}7.$ Assume that in the initial state, the interior cavity of the cylindrical piston system holding the gas is $5$ cm high and $5$ cm in radius. The radius of the sprocket is $3\mathrm{.}1831$ cm $.$ The initial temperature of the gas is $400$ K and its initial pressure is $10$ atm $.$ After a reversible adiabatic expansion over a certain span, the work performed is $472\mathrm{.}1$ J $.$ The mass is $13\mathrm{.}958$ kg $.$ Assume at the start of the expansion, the weight is hung from a point on the cam extending horizontally to the right

of the pivot point. Write a Matlab program to calculate and plot the shape of the cam required to facilitate the reversible process. Assume the pivot point of the cam is the origin of the coordinate system. Write out the logic and calculations used to solve the problem.

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