The Seebeck voltage (?) to relative temperature (T) conversion for a copper-constantan thermocouple with an ice point (0.00°C) reference is given over the range -160.°C to 400.°C by T = a0 a1? + a2?2 + a3?3 + ... + a7?7 , where T is in °C and ? is the Seebeck voltage in microvolts (i.e., 10-6 V). The polynomial coefficients given by the National Bureau of Standards are
a0 = 0.100860910
a1 = 25727.94369
a2 = -767345.8295
a3 = 78025595.81
a4 = -9247486589
a5 = 6.97688 × 1011
a6 = -2.66192 × 1013
a7 = 3.94078 × 1014
a. Write an interactive computer program that asks the user for the thermocouple voltage (in the proper units) and returns the temperature, Seebeck, Peltier, and difference in Kelvin coefficients (in proper units) to the screen.
b. Plot the Seebeck voltage and the Seebeck and Peltier coefficients vs. temperature over the temperature range of 100.°C to 400.°C using at least 100 points per curve.