"HEAT CAPACITY, POWER SERIES APPROXIMATION, SIMULTANEOUS EQUATIONS. The heat capacity of a gas, Cp or Cv, can be predicted an any temperature T (Note: T must be within the limits of the experimental data used to calculate the constants) by a power series of the form: Cp = a + b*T +c*T^2 + d*T^3. Cp is a linear function of the constants (a, b, c and d) but not of the temperature T! To calculate the constants (a, b, c and d), one needs to measure Cp[i] at 4 different temperatures T[i]. *** Answer(s) to Problem(s) **** (c) Copyright PCSCC, Inc., 1993The equations and variables are included. It is desired to solve for the constants A, B, C and D. To solve a set of linear simultaneous equations, there must be 4 linearly independent equations in four unknowns. The variables T[I] are made inactive (no equal sign) and are not used by the S function. Set the values of Cp[1], Cp[2], Cp[3] andCp[4]. Type S to solve as linear. The results are A=9.3, B=0.12, C=-6.8e-5 and D=1.6e-8. Type any key to exit. ||Calculate the 4 constants (a, b, c and d) needed to approximatethe heat capacity of methyl chloride gas by a power series of the form Cp=a+b*t+c*T^2+d*T^3. Measurements of the heat capacities (J/K/mole) at 4 different temperatures (in K) yield the following data in (T,Cp) pairs: (400,48.10), (600,61.25), (800,71.26), (1000,78.90). (from Warn, J. R. W., Concise Chemical Thermodynamics, van Nostrand Reinhold, London, 1969) Type comma key to see entire comment. Type (F2) to return to application file."
