Question

Write down the temperature of (i) lower fixed point, and (ii) upper fixed point, on the Fahrenheit scale.

Answer 1

Hint: The lower fixed point is defined as the melting point of ice (solid state of water) which is equal to ${{0}^{\circ }}C$ and the upper fixed point is defined as the boiling point of water and it is equal to ${{100}^{\circ }}C$. Here, we will convert these temperatures from degree Celsius to degree Fahrenheit. This can be done using the formula: $^{\circ }C\times \left( \dfrac{9}{5} \right)+32{{=}^{\circ }}F$.

Complete answer:
We will solve both the parts of our question one by one. Let us start by solving the first part.
(i) The lower fixed point is equal to ${{0}^{\circ }}C$. Let this temperature be denoted by ‘m’ in degree Celsius and ‘X’ in degree Fahrenheit.
Now, we can use the formula for conversion of any temperature in Celsius to Fahrenheit. This can be done as follows:
$\Rightarrow {{m}^{\circ }}C\times \left( \dfrac{9}{5} \right)+32={{X}^{\circ }}F$
Now, putting the value of ‘m’ in above equation and solving for ‘X’, we get:
$\begin{align}
  & \Rightarrow {{0}^{\circ }}C\times \left( \dfrac{9}{5} \right)+32={{X}^{\circ }}F \\
 & \therefore X={{32}^{\circ }}F \\
\end{align}$
Thus, the temperature of the lower fixed point comes out to be ${{32}^{\circ }}F$.
(ii) The upper fixed point is equal to ${{100}^{\circ }}C$. Let this temperature be denoted by ‘n’ in degree Celsius and ‘Y’ in degree Fahrenheit.
Now, we can use the formula for conversion of any temperature in Celsius to Fahrenheit. This can be done as follows:
$\Rightarrow {{n}^{\circ }}C\times \left( \dfrac{9}{5} \right)+32={{Y}^{\circ }}F$
Now, putting the value of ‘n’ in above equation and solving for ‘Y’, we get:
$\begin{align}
  & \Rightarrow {{100}^{\circ }}C\times \left( \dfrac{9}{5} \right)+32={{X}^{\circ }}F \\
 & \Rightarrow Y={{\left( 180+32 \right)}^{\circ }}F \\
 & \therefore Y={{212}^{\circ }}F \\
\end{align}$
Thus, the temperature of the upper fixed point comes out to be ${{212}^{\circ }}F$.
Hence, the temperature of (i) lower fixed point, and (ii) upper fixed point, on the Fahrenheit scale comes out to be ${{32}^{\circ }}F\text{ and 21}{{\text{2}}^{\circ }}F$ respectively.

Note:
One should always know the formula for these basic conversions. The most important conversions are between, Kelvin, Celsius and Fahrenheit. It is also important to remember the definition of terms like, lower fixed point and upper fixed point as they are some very important notations used in Physics.