Question

A Centigrade and Fahrenheit thermometers are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers a temperature of $140{}^{\circ }\text{F}$. The fall of the temperature as registered by the centigrade thermometer is:

• A. $40{}^{\circ }\text{C}$
• B. $80{}^{\circ }\text{C}$
• C. $50{}^{\circ }\text{C}$
• D. $90{}^{\circ }\text{C}$

Answer 1

The correct option is A $40{}^{\circ }\text{C}$

Given,
Initial temperature in Celsius, $T_i=100{}^{\circ }\text{C}$
[temperature of boiling water]
Final Reading of temperature in Fahrenheit, $T_f=140{}^{\circ }\text{F}$
Final temperature in Celsius, $T_c=?$
We know the relation between Celsius and Fahrenheit scale,
$\frac{T_c}{100}=\frac{T_f-32}{180}$
$\Rightarrow \frac{T_c}{100}=\frac{140-32}{180}$
$\Rightarrow T_c=60{}^{\circ }\text{C}$
So, fall of temperature in Celsius is
$T_i-T_c=100-60={40}^{\circ }\text{C}$