Question

State the temperature of the ice point and the steam point on the Fahrenheit scale:
A. ice point =${{32}^{o}}F$, stream point = ${{212}^{o}}F$
B. Ice point =${{22}^{o}}F$, stream point = ${{200}^{o}}F$
C. ice point = ${{30}^{o}}F$stream point = ${{210}^{o}}F$
D. ice point = ${{20}^{o}}F$stream point = ${{200}^{o}}F$

Answer 1

By the definition of the ice point it is the temperature at which a mixture of ice and the water are in equilibrium at a pressure of the one atmosphere and it is ${{0}^{o}}C$ so we have to use the relation between Celsius and Fahrenheit to get temperature in the unit of the Fahrenheit and the same method will be used for the stream point.

Formula used:
$F=C\times \dfrac{9}{5}+32$

Complete step by step solution:
Ice point: The temperature at which a mixture of the ice and the water are in the equilibrium at a pressure of the one atmosphere it is ${{0}^{o}}C$on the Celsius scale.
Now let’s convert Celsius to the Fahrenheit using the below stated equation. $F=C\times \dfrac{9}{5}+32.....\left( 1 \right)$
Where, C is the temperature in the Celsius
F is the temperature in the Fahrenheit

Now as we know that temperature of the ice point in the Celsius is${{0}^{o}}C$, so let’s put the value in the equation (1)
$\begin{aligned} & \Rightarrow F=0\times \dfrac{9}{5}+32 \\\ & \therefore F={{32}^{o}}F \\\ \end{aligned}$

Therefore the temperature of the ice point on the Fahrenheit scale is${{32}^{o}}F$.

Now stream point,
Stream point:
The temperature at which water vapor condenses at a pressure at one atmosphere and on the Celsius scale the temperature of the stream point is${{100}^{o}}C$

Now let’s convert the temperature given in the degree Celsius to the temperature in the Fahrenheit using the equation (1)
$\begin{aligned} & \Rightarrow F=100\times \dfrac{9}{5}+32 \\\ & \Rightarrow F=180+32 \\\ & \therefore F={{212}^{o}}F \\\ \end{aligned}$

Therefore temperature of the stream point on the Fahrenheit scale is ${{212}^{o}}F$

Hence, the option (A) is correct.

Note:
There are two simple tricks for remembering the formula that is stated in the solution.
(1) Use directly 1.8 instead of $\dfrac{9}{5}$
$\begin{aligned} & F=C\times 1.8+32\text{ } \\\ & \left( or \right) \\\ & F=1.8C+32 \\\ \end{aligned}$
(2) Remember formula in the form at the statement i.e.
$^{o}C\text{ to}{{\text{ }}^{o}}F$ Divide by 5, then multiply by 9 them add by 32
(or) ÷ by 5,× by 9 and them + 32