Question

What is 75 degrees Fahrenheit converted into Celsius and Kelvin?

Answer 1

Hint: Temperature is the degree of hotness or the coldness of a body which more precisely determines the flow of heat from one body to another when placed in contact. The temperature is measured on different scales according to the convenience. The temperature obtained on one scale can be converted to some other scale as measure of temperature on various scales is just a matter of division of the scale from ice point to boiling point into equal divisions. Hence using the relation between the temperature of a body on various scales, we can obtain the temperature on a preferable scale.
Formula used:
$\dfrac{{{T}_{C}}-0}{100-0}=\dfrac{{{T}_{F}}-32}{212-32}=\dfrac{{{T}_{K}}-273.15}{373.15-273.15}$

Complete answer:
The range between two fixed temperatures is called the fundamental interval, which divided into a suitable number of equal divisions forms a thermometric scale.
The Celsius scale has a lower fixed point (ice point) is taken as ${{0}^{\circ }}C$ and the upper fixed point (steam point) as ${{100}^{\circ }}C$ . the interval between the two fixed points is divided into hundred equal parts and each part is 1 degree Celsius.
On the Fahrenheit scale the lower fixed point is ${{32}^{\circ }}F$ and the upper fixed point is ${{212}^{\circ }}F$ . the interval between them is divided into 180 equal parts and each part is 1 degree Fahrenheit.
Similarly on the Kelvin scale, the lower fixed point is taken as 273.15 K and the upper fixed point as373.15K. The interval between them is divided into 100 equal parts and each part is equal to 1 Kelvin.
Let us say the measured temperature on the Kelvin scale be ${{T}_{K}}$ , on the Celsius scale be ${{T}_{C}}$ and on the Fahrenheit scale be ${{T}_{F}}$ . Hence using the above information the relation between the temperature on their respective scale is,
$\dfrac{{{T}_{C}}-0}{100-0}=\dfrac{{{T}_{F}}-32}{212-32}=\dfrac{{{T}_{K}}-273.15}{373.15-273.15}$
In the question we are asked to convert 75 degrees Fahrenheit into Celsius and Kelvin. Hence using the above relation the same temperature on the Celsius scale is,
$\begin{align}
  & \dfrac{{{T}_{C}}-0}{100-0}=\dfrac{{{T}_{F}}-32}{212-32} \\
 & \Rightarrow \dfrac{{{T}_{C}}}{100}=\dfrac{75-32}{212-32}=0.2388 \\
 & \therefore {{T}_{C}}={{23.88}^{\circ }}C \\
\end{align}$
Similarly the temperature on the Kelvin scale is,
$\begin{align}
  & \dfrac{{{T}_{F}}-32}{212-32}=\dfrac{{{T}_{K}}-273.15}{373.15-273.15} \\
 & \Rightarrow \dfrac{75-32}{212-32}=\dfrac{{{T}_{K}}-273.15}{373.15-273.15} \\
 & \Rightarrow \dfrac{{{T}_{K}}-273.15}{100}=0.2388 \\
 & \Rightarrow {{T}_{K}}-273.15=23.88 \\
 & \Rightarrow {{T}_{K}}=23.88K+273.15K \\
 & \therefore {{T}_{K}}=297.03K \\
\end{align}$
Therefore the value of temperature of 75 degree Fahrenheit is equal to 23.88 degree Celsius on the Celsius scale and 297.03K on the Kelvin scale

Note:
It is to be noted all the scales have their own significance. These scales are basically there due to their preference in various experiments. One can also solve the above problem by obtaining the relation between the value of single division on their respective scales.