Question

You work in a materials testing lab and your boss tells you to increase the temperature of a sample by 31.5 ∘C . The only thermometer you can find at your workbench reads in degrees Fahrenheit.

(A)

If the initial temperature of the sample is 68.5 ∘F, what is its temperature in degrees Fahrenheit when the desired temperature increase has been achieved?

Express your answer in degrees Fahrenheit to three significant figures.

Answer 1

Initial temperature in Fahrenheit = T_f1 = 68.5 ^oF

Initial temperature in Celsius = T_c1

T_f1 = 1.8T_c1 + 32

68.5 = 1.8T_c1 + 32

T_c1 = 20.278 ^oC

Final temperature in Fahrenheit = T_f2

Final temperature in Celsius = T_c2

Increase in temperature of the sample in Celsius = T_c = 31.5 ^oC

T_c = T_c2 - T_c1

31.5 = T_c2 - 20.278

T_c2 = 51.778 ^oC

T_f2 = 1.8T_c2 + 32

T_f2 = (1.8)(51.778) + 32

T_f2 = 125.2 ^oF

Rounding off to two three significant figures,

T_f2 = 125 ^oF

A) Temperature in Fahrenheit when the desired temperature increase has been achieved = 125.2 ^oF