The van der waals equation of state is perhaps the best-known approximate equation of state for a non-ideal gas, but various other parameterized functional forms for gas-phase equations of state have also been suggested. calculate (i) the isothermal compressibility kt -(op)t n and(ii) the (volumetric) expansivity av-v ( at (also known as the coefficient of thermal expansion) for: (a) a fluid governed by the berthelot equation of state, given by: p = anr- , for some constant parameters a and b; and then (b) a gas following the dieterici equation of state: p kt, for some fixed parameters a and b (b a gas folowing the dietena equation of state: p = kt e ke tv for some fixed parameters a and b (not necessarily the same in the two different cases). yes, you can use a program like mathematica or matlab if you wish notice that both equations of state reduce to the ideal gas law in the limit where a -> 0 and b -0 so as a good sanity check, verify explicitly that your answers for the response functions reduce to the ideal-gas results in this limit. hint: it will be easier if you do not try to solve explicitly for v(t, p, n), but use implicit differentiation