A thermostat control with dial markings from 0 to 200 is used to regulate the te

Question

A thermostat control with dial markings from 0 to 200 is used to regulate the temperature of an oil bath.
please help

Problem 3.66 Thermostat Your answer is partially correct. Try again. A thermostat control with dial markings from 0 to 200 is used to regulate the temperature of an oil bath. A calibration plot on logarithmic coordinates of the temperature PF versus the dial setting R is a straight line that passes through the points R1 a. In the equation T("F) = ARD, what are the values of A and b? 15.0 T1-110 0F) and R2=60.0 T2 250.0F 194.42 A= b. Estimate the thermostat setting need to obtain a temperature of 360.0°F R = 111.83 c. Estimate the thermostat setting needed to obtaln a temperature of 120.0°C 17.383

Explanation / Answer

Solve the equation in terms of logarithmic

ln T = b ln(AR) = b ln A + b ln R

At T = 110 F,

R = 15

ln 110 = 0.59* ln A + 0.59* ln 15

3.1027 = 0.59* ln A

ln A = 5.2588

A = 192.25 °F

Part c

T = 120°C = 248 °F

ln T = b ln A + b ln R

ln T1 = b ln A + b ln R1

Subtract the equations

ln (T/T1) = b ln (R/R1)

ln (248/110) = 0.59 * ln (R/15)

1.37787 = ln (R/15)

R = 15 * 3.966

R = 59.496

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