The heat capacity of dimethylacetylene can be modeled in the range T = 200 K to 1200 K as CP(T) = A + BT + CT^2 + DT^3 + ET^4 , where CP is in J/molK and T in K, with A =1.21x10^(1) , B=2.82x^(10-1) , C=-1.77x^(10-4) , D=5.56x10^(-8) , and E=-6.35 x10^(-12).

If we assume the functional form is sufficiently close to reality, then the main source of error will be in the coefficients A-E. Assume each of the these coefficients contains 3% relative error and that there is random error in the experimental measurement of the temperature with magnitude approximately 1 degree, independent of the temperature. a. At T=200 and T=1200, what will be the absolute and relative error in CP? (Note that T=200 and T=1200 is what we measure the temperature as, there is still 1 degree error to what it actually is).

b) Now assume the temperature is exact, and there is only error in the physical constants A through E. Which of these five coefficients would be most important to determine more precisely if we are interested in accurately predicting heat capacities at temperatures at the lower range? Which coefficient would we most want to determine more precisely if we are interested in temperatures in the upper range?