Suppose we do high quality measurements of Cp for a given material as a function

Question

Suppose we do high quality measurements of Cp for a given material as a function of temperature at standard pressure. (NIST uses a standard temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 101.325 kPa (14.696 psi) as a reference point. If we have values at those points, then we can calculate changes to find the dependence on temperature and pressure.) We take take data from T=300 K to 600 K and find that we can fit that data to the form (an approximation to the Debye function): Cp 18.912 + 0.0181066 T - 0.0000150298 T^2 Based on this form, calculate the enthalpy and entropy as a function of temperature (use values T = 400 K, 500 K, 600 K). Units of Cp are J/K.

Explanation / Answer

let Cp=A+B*T+C*T^2

where A=18.912

B=0.0181066

C=-0.0000150298

then enthalpy=integration of Cp*dT

=integration of (A+B*T+C*T^2)*dT

=A*T+0.5*B*T^2+(C/3)*T^3

=18.912*T+0.0090533*T^2-5.093333*10^(-6)*T^3

entropy=integration of Cp*dT/T

=integration of (A+B*T+C*T^2)*dT/T

=A*ln(T)+B*T+0.5*C*T^2

=18.912*ln(T)+0.0181066*T-0.0000075149*T^2

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