Chapter 18, Problem 1P

(a)

To determine

The absolute zero in the new scale.

Answer to Problem 1P

The absolute zero in the new scale is $-738°\text{N}$.

Explanation of Solution

Given info: The normal human body temperature in degree Fahrenheit is $98.6°\text{F}$. In the new scale the normal body temperature and freezing point of water is $100°\text{N}$ and $0°\text{N}$ respectively. The melting point of mercury is $-37.9°\text{F}$. The highest temperature is $134.1°\text{F}$.

Write the expression to convert the temperature scale.

$N=aF+b$ (1)

Here,

$N$ is the temperature in $°\text{N}$.

$a,b$ are constants.

$F$ is the temperature in degree Fahrenheit.

Substitute $98.6°\text{F}$ for $F$ and $100°\text{N}$ for $N$ in equation (1).

$100°\text{F}=a\left(98.6°\text{F}\right)+b$ (2)

The freezing point of water in degree Fahrenheit is $32°\text{F}$.

Substitute $32°\text{F}$ for $F$ and $0°\text{N}$ for $N$ in equation (1).

$0\text{N}=a\left(32°\text{F}\right)+b$ (3)

Solve equation (2) and (3).

$\begin{array}{c}a=1.5\\ b=-48.04\end{array}$

The temperature of absolute zero in degree Fahrenheit is $-460$.

Substitute $-460$ for $F$, $1.5$ for $a$ and $-48.04$ for $b$ in equation (1).

$\begin{array}{c}N=1.5\left(-460\right)+\left(-48.04\right)\\ =-738\text{N}\end{array}$

Conclusion:

Therefore, the absolute zero in the new scale is $-738°\text{N}$.

(b)

To determine

The melting point of mercury in new scale.

Answer to Problem 1P

The melting point of mercury in new scale is $-105°\text{N}$.

Explanation of Solution

Given info: The normal human body temperature in degree Fahrenheit is $98.6°\text{F}$. In the new scale the normal body temperature and freezing point of water is $100°\text{N}$ and $0°\text{N}$ respectively. The melting point of mercury is $-37.9°\text{F}$. The highest temperature is $134.1°\text{F}$.

Write the expression to convert the temperature scale.

$N=aF+b$ (1)

Substitute $-37.9$ for $F$, $1.5$ for $a$ and $-48.04$ for $b$ in equation (1).

$\begin{array}{c}N=1.5\left(-37.9\right)+\left(-48.04\right)\\ =-105\end{array}$

Conclusion:

Therefore, the melting point of mercury in new scale is $-105°\text{N}$.

(c)

To determine

The boiling point of water in new scale.

Answer to Problem 1P

The boiling point of water in new scale is $270°\text{N}$.

Explanation of Solution

Given info: The normal human body temperature in degree Fahrenheit is $98.6°\text{F}$. In the new scale the normal body temperature and freezing point of water is $100°\text{N}$ and $0°\text{N}$ respectively. The melting point of mercury is $-37.9°\text{F}$. The highest temperature is $134.1°\text{F}$.

The boiling point of water in degree Fahrenheit is $212$.

Write the expression to convert the temperature scale.

$N=aF+b$ (1)

Substitute $212$ for $F$, $1.5$ for $a$ and $-48.04$ for $b$ in equation (1).

$\begin{array}{c}N=1.5\left(212\right)+\left(-48.04\right)\\ =270\end{array}$

Conclusion:

Therefore, the boiling point of water in new scale is $270°\text{N}$.

(d)

To determine

The highest recorded air temperature on Earth’s surface in new scale.

Answer to Problem 1P

The highest recorded air temperature on Earth’s surface in new scale is $153°\text{N}$.

Explanation of Solution

Given info: The normal human body temperature in degree Fahrenheit is $98.6°\text{F}$. In the new scale the normal body temperature and freezing point of water is $100°\text{N}$ and $0°\text{N}$ respectively. The melting point of mercury is $-37.9°\text{F}$. The highest temperature is $134.1°\text{F}$.

Write the expression to convert the temperature scale.

$N=aF+b$ (1)

Substitute $134.1$ for $F$, $1.5$ for $a$ and $-48.04$ for $b$ in equation (1).

$\begin{array}{c}N=1.5\left(134.1\right)+\left(-48.04\right)\\ =153\end{array}$

Conclusion:

Therefore, the highest recorded air temperature on Earth’s surface in new scale is $153°\text{N}$.