Question

If the temperature is ${95^ \circ }F$, what is the temperature in Celsius?
A. $55{}^ \circ C$
B. $35{}^ \circ C$
C. $20{}^ \circ C$
D. $52{}^ \circ C$

Answer 1

The temperature in a thermometer can be measured either in Fahrenheit or Celsius and these two measurements are related to each other as well. The formula relating the temperature of the thermometer in Fahrenheit and Celsius is applied in-order to determine the correct value of the temperature in the Celsius using the value of temperature in Fahrenheit.

Formula used:
The equation relating the temperature in Fahrenheit and Celsius is given to be:
${T_c} = \dfrac{5}{9}\left( {{T_f} - 32} \right)$
Where, ${T_c}$ denotes the temperature in Celsius and ${T_f}$ denotes the temperature in Fahrenheit.

Complete step by step answer:
The above problem revolves around the concept of conversion of temperature from Fahrenheit to Celsius. Before we do this conversion we first need to know how temperatures are measured and the relation that relates the units of temperature which is Fahrenheit and Celsius.

A thermometer is a device that measures the temperature of a body. The thermometer makes use of some measurable quantity which is called as the thermometric property of a substance which changes linearly with temperature. It is a measure or the degree of how hot or cold the body is. Heat is a quantity which flows from higher temperature to lower temperature.

The thermometer can be used to measure the temperature using different scales like the Fahrenheit scale, the Celsius scale and the Kelvin scale. All these thermometers measure the same temperature value but on different scales. This means that all of these scales measure the same temperature but the value of the measured temperature will vary from one scale to another but all of them actually have the same temperature.

Hence we can say that there is a relation between the scales of measurements. Here, the question mentions the Fahrenheit and the Celsius scales only so the first step is to determine the equation relating the two scales. The equation is as follows:
$\dfrac{C}{{100}} = \dfrac{{F - 32}}{{180}}$

This equation is derived from the concept of equating the temperature differences between the highest points of the Celsius and Fahrenheit scales and the lowest points of the scales. This equation is further simplifies in-order to get:
$\dfrac{C}{5} = \dfrac{{F - 32}}{9}$
By cross multiplying the terms and rearranging the terms to make $C$ as the subject we get the common equation relating the two scales.
$C = \dfrac{5}{9}\left( {F - 32} \right)$
We replace $C$ and $F$ with the temperature measured by the Celsius scale as ${T_c}$ and the temperature measured by the Fahrenheit scale as ${T_f}$ respectively we get the equation to be:
${T_c} = \dfrac{5}{9}\left( {{T_f} - 32} \right)$ ------($1$)

We are given that the value of the temperature in the Fahrenheit scale is ${95^ \circ }F$. We are asked the temperature in the Celsius scale and hence we substitute the Fahrenheit value of temperature in the above equation ($1$) in order to get the temperature in Celsius scale. Hence we have:
${T_c} = \dfrac{5}{9}\left( {95 - 32} \right)$
On solving further we get:
$\Rightarrow {T_c} = \dfrac{5}{9}\left( {63} \right)$
$\Rightarrow {T_c} = 5 \times 7$
$\therefore {T_c} = 35{}^ \circ C$
This is the temperature in Celsius equivalent to the Fahrenheit value in the Fahrenheit scale.

Therefore, the correct answer is option B.

Additional information: Temperature is a quantity that is said to be defined as the thermal state of the body which decides the direction of flow of heat energy from one body to another when they are placed in thermal contact with each other. A thermometer is named after a Latin word ‘thermo’ which means heat and ‘meter’ which means measurement and the device was invented back in 1612.

Note: The Celsius scale is used everywhere across the globe. This scale is also known as the centigrade scale which was devised based on the degree of freezing and boiling point of water which is ${0^ \circ }$ and ${100^ \circ }$ respectively. These two scales are derived from the Kelvin scale.