Answer to Question #234074 in Mechanical Engineering for Randal Rodriguez

Question

11. A Fahrenheit and a Celsius thermometer are both immersed in a fluid. a) If the two numerical readings

are identical, what is the temperature of the fluid expressed in o K and o R. b) If the Fahrenheit

temperature is numerically twice that of the Celsius reading, what is the temperature of the fluid

expressed in o K and o R?

Answer 1

Fahrenheit and Celsius degrees can be interconverted through the formulae

$\degree F=\frac{9}{5}(\degree C)+32$

a)

To have the same value;

Let °C=x, then °F=x

$x=\frac{9}{5}x+32$

$x-\frac{9}{5}x=32$

$-\frac{4}{5}x=32$

-4x=32*5

x$=\frac{160}{-4}$

x=-40

Thus, -40°C=-40°F

°K=°C+273.15

=-40+273.15

=233.15°K

°R=°F+459.67

=-40+459.67

=419.67°R

b)

°F is twice °C

Let °C=x, $\therefore$ °F=2x

2x=$\frac{9}{5}x+32$

$2x-\frac{9}{5}x=32$

$\frac{1}{5}x=32$

x=32*5=160

Thus 160°C=320°F

°K=°C+273.15

=160+273.15

=433.15°K

°R=°F+459.67

=320+459.67

=779.67°R