Problem 3.66 Thermostat Your answer is partially correct. Try again. A thermosta

Question

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 (R1-15.0, T1 = 110.0°F) and (R2-60.0, T2=250.0 a. In the equation T(°F) = ARb, what are the values of A and b? . 3.8 b = 1.59 b. Estimate the thermostat setting need to obtain a temperature of 360.0°F 27.11 c. Estimate the thermostat setting needed to obtain a temperature of 120.0°C 20.49 R-

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

4.7 - 1.59 = 0.59* ln A

ln A = 5.27

A = 194.42 °F

Part b

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 (360/110) = 0.59 * ln (R/15)

1.1856/0.59 = ln (R/15)

2.009 = ln (R/15)

R = 15 * 7.455

R = 111.83

Part c

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

ln (120/110) = 0.59 * ln (R/15)

0.087/0.59 = ln (R/15)

0.14747 = ln (R/15)

R = 15 * 1.158

R = 17.383

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