Question

The normal human body temperature is $98.4°\text{F}$. If the body temperature of a person is $313\text{K}$, then the person .

• A. has normal temperature
• B. has a high fever.
• C. has a temperature less than normal temperature.
• D. nothing can be said about his health condition.

Answer 1

The correct option is B

has a high fever.

Step 1: Given Data and assumption:

Normal human body temperature is $T_N=98.4°\text{F}$.

The mentioned person has a body temperature ${\theta }_P=313\text{K}$.

Assume that the temperature of the person on the Kelvin scale is $T_P$.

Step 2: Conversion Formula among temperature scales:

Recall the conversation relation between Kelvin and Fahrenheit scale:

Let, $\theta$ is the temperature of a substance on the Kelvin scale, and $T$ is the temperature of the same substance on the Fahrenheit scale. These two are related as:

$T=\frac{9}{5}\left(\theta -273\right)+32$

Step 3: Calculation:

Converting the temperature of the person on the Fahrenheit scale:

$T_P=\frac{9}{5}\left({\theta }_P-273\right)+32$

Substitute $313\text{K}$ for ${\theta }_P$:

$\begin{array}{rcl}{T}_P& =& \left[\frac{9}{5}\left(313-273\right)+32\right]°\text{F}\\ & =& 104°\text{F}\end{array}$

Thus, $T_P>T_N$

Therefore, the person has a high fever.

Hence, the correct option is B.