Question

Convert \[100^\circ F\] into Celsius and Kelvin scale of temperature.

Answer 1

Hint: We will write the expression for relation between Kelvin scale temperature and Fahrenheit scale temperature. We will also use the relation between Celsius scale temperature and Fahrenheit scale temperature.

Complete step by step answer:
Let us write the expression for the relation between Celsius and Fahrenheit scale.
\[C = \dfrac{5}{9}\left( {F - 32} \right)\]
Here C represents the temperature in Celsius, and F represents the temperature in Fahrenheit.

On substituting 100 for F in the above expression, we get:
\[\begin{array}{l}
C = \dfrac{5}{9}\left( {100 - 32} \right)\\
 = 37.78
\end{array}\]

The value of temperature obtained from the above expression is in degree Celsius, so we can write:
\[C = 37.78^\circ {\rm{C}}\]

We can write the expression for relation between Kelvin and Fahrenheit scale.
 \[K = \dfrac{5}{9}\left( {F - 32} \right) + 273.15\]
Here K represents the value of temperature in the Kelvin scale.

On substituting 100 for F in the above expression, we get:
\[\begin{array}{c}
K = \dfrac{5}{9}\left( {100 - 32} \right) + 273.15\\
K = 310.92{\rm{ K}}
\end{array}\]

Therefore, we can say that the Celsius scale's value is \[37.78^\circ {\rm{C}}\] and on the Kelvin scale is \[310.92{\rm{ K}}\].

Additional Information:
Scientists always use the Kelvin scale because it starts at absolute zero. Zero Kelvin means the zero kinetic energy, and we know that kinetic energy is directly proportional to temperature. Hence, if there is a doubling of Kelvin temperature, then it means that the system's kinetic energy is doubled.

Note:
Rather than writing the expression for relation between Kelvin and Fahrenheit scale, we can write the relation between Kelvin and Celsius scale to find the given temperature value in Kelvin. We can also use the linear interpolation method, but we should remember the ice point and steam point of different scales of temperature.