Question

A Centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers a temperature of 1400. The fall of the temperature as registered by the Centigrade thermometer is:
A. 400
B. 800
C. 500
D. 900

Answer 1

Use the relation between Centigrade and Fahrenheit to find the temperature fall.

Formula used: $\dfrac{C}{5}=\dfrac{F-32}{9}$
Here
$C$ is the temperature in Centigrade
$F$ is the temperature in Fahrenheit

Complete step by step solution:
The temperature registered in the Fahrenheit thermometer is 1400
Substituting in the formula
$\begin{aligned} & \dfrac{C}{5}=\dfrac{140-32}{9} \\\ & \dfrac{C}{5}=\dfrac{108}{9} \\\ & C={{60}^{0}} \\\ \end{aligned}$

The temperature of boiling water is 1000
The temperature drop measured is
$\Delta C={{100}^{0}}-{{60}^{0}}={{40}^{0}}$

The correct answer is option A.

Additional information: In the Centigrade thermometer the freezing point of water was referenced at 00 and the boiling point at 1000 initially. The definition used for Centigrade scale now uses the triple point of water, the temperature at which all the three phases coexist.
The SI unit of thermodynamic temperature is Kelvin ($K$). Absolute zero, the lowest temperature possible is defined at exactly $0K\text{ or -273}\text{.1}{{\text{5}}^{0}}C$.

Note: The temperature at which both the Centigrade and Fahrenheit thermometers show the same value is $C=F=-{{40}^{0}}$.