A thermostat control with dial markings from 0 to 100 is used to regulate the temperature of

Question:

A thermostat control with dial markings from 0 to 100 is used to regulate the temperature of an oil bath. A calibration plot on logarithmic coordinates of the temperature, T(?F) versus the dial setting, R, is a straight line that passes through the points (R1 = 20.0, T1 = 110.0?F) and (R2 = 40.0, T2 = 250.0?F).

(a) Derive an equation for T (?F) in terms of R.

(b) Estimate the thermostat setting needed to obtain a temperature of 320?F.

(c) Suppose you set the thermostat to the value of R calculated in part (b) and the reading of a thermocouple mounted in the bath equilibrates at 295?F instead of 320?F. Suggest several possible explanations.