Question

Calculate the temperature of a fluid when both a Fahrenheit and a Celsius thermometer are immersed in it, under the following conditions :a) the numerical reading is identical in both thermometers? b) the Fahrenheit reading is numerically twice that of the Celsius reading. Express the values in °R and °K.

Answer 1

The connection between two temperature units is following

$\displaystyle T_C = (T_F -32) \cdot \frac{5}{9}$

(a) let's denote X the number we are looking for

$\displaystyle X = \frac{5}{9}(X-32) = \frac{5}{9} X -17.7778$

$\displaystyle \frac{4}{9} X = -17.7778$

$X =-40$

Answer: $T_F = -40^\circ F, T_C = -40^\circ C, T=233.15 K$

(b) let's denote Celsius temperature as X

$\displaystyle X = \frac{5}{9}(2X-32) = \frac{10}{9} X -17.7778$

$\displaystyle -\frac{1}{9} X = -17.7778$

$X=160$

Answer: $T_F = 320^\circ F, T_C = 160^\circ C, T=433.15 K$