Q1PE - College Physics (Urone)

Question

What is the Fahrenheit temperature of a person with a 39.0ºC fever

Step-by-Step Solution

Answer

A person with a temperature of  \({\rm{39}}{\rm{.0^\circ C}}\) has the equal temperature as \(102.2^\circ {\rm{F}}\)  on the Fahrenheit scale.

Step 1: Difference between Fahrenheit and Celcius

You need to find the Celcius corresponding Fahrenheit temperature. So the relation between the two-scale is,

$\begin{array}{rcl}\mathbf{C}& \mathbf{=}& \frac{\mathbf{5}}{\mathbf{9}}\mathbf{(}\mathbf{F}\mathbf{-}\mathbf{32}\mathbf{)}\\ \mathbf{C}\mathbf{\times }\frac{\mathbf{9}}{\mathbf{5}}& \mathbf{=}& \mathbf{(}\mathbf{F}\mathbf{-}\mathbf{32}\mathbf{)}\end{array}$

Step 2: Calculation

When T= \({\rm{39}}{\rm{.0^\circ C}}\) , Substituting this into the above equation, we get,

$\begin{array}{rcl}\mathbf{39}\mathbf{.}\mathbf{0}\mathbf{°}\mathbf{C}\mathbf{\times }\frac{\mathbf{9}}{\mathbf{5}}& \mathbf{=}& \left(F-32\right)\\ \mathbf{70}\mathbf{.}\mathbf{2}\mathbf{°}\mathbf{C}& \mathbf{=}& \mathbf{F}\mathbf{-}\mathbf{32}\\ \mathbf{F}& \mathbf{=}& \mathbf{102}\mathbf{.}\mathbf{2}\mathbf{°}\mathbf{F}\end{array}$

Therefore, a person with a temperature   \({\rm{3}}{{\rm{9}}^{\rm{o}}}{\rm{C}}\)  has the same temperature as a person with a temperature \({\rm{10}}{{\rm{2}}^{\rm{o}}}{\rm{F}}\)   on the Fahrenheit scale. Thermometers are used to measure temperature on well-defined measurement scales. Different temperature scales can be developed by finding easily  2  reproducible temperatures, such as freezing and boiling water at standard atmospheric pressure.