Chapter 1.1, Problem 98E

a.

To determine

To find: The relationship between degree Celsius C and Fahrenheit F .

Answer to Problem 98E

The relationship between degree Celsius C and Fahrenheit F is $\frac{C}{100}=\frac{F-32}{180}$ .

Explanation of Solution

Given:

Water freezes at $0C\left({32}^{0}F\right)$ and boils at $100C\left({212}^{0}F\right)$

Formula/ concept used:

The temperature on Celsius and Fahrenheit scales is shown in Figure-1.

  

Calculations:

Let C and F be the same temperature on the Celsius and Fahrenheit scales respectively.

The linear characteristics of the Celsius scale is $\frac{C-0}{100-0}$ , and the linear characteristics of the Fahrenheit scale is $\frac{F-32}{212-32}$ .

Two scales will be identical when linear characteristics of both scales is same, i.e., $\frac{C-0}{100-0}=\frac{F-32}{212-32}$

  $\frac{C}{100}=\frac{F-32}{180}$ ........ (1)

This is the relationship between degree Celsius C and Fahrenheit F .

Conclusion:

The relationship between degree Celsius C and Fahrenheit F is $\frac{C}{100}=\frac{F-32}{180}$ .

b.

To determine

To complete: A given table using equation of part (a).

Answer to Problem 98E

The completed table is

C	17.780	-100	100	200	500	1770
F	00	140	320	680	900	350.60

Explanation of Solution

Given:

The given table is

C		-100	100			1770
F	00			680	900	350.60

Concept used:

The equation obtained in part (a).

Calculations:

The relationship between Celsius and Fahrenheit scale is $\frac{C}{100}=\frac{F-32}{180}$ .

Now, $\frac{C}{100}=\frac{0-32}{180}\Rightarrow C={17.78}^{0}C$

Now, $\frac{-{10}^{0}C}{100}=\frac{F-32}{180}$

  $\Rightarrow F={14}^{0}C$

Now, $\frac{{10}^{0}C}{100}=\frac{F-32}{180}$

  $\Rightarrow F={50}^{0}C$

  $\frac{{}^{0}C}{100}=\frac{68-32}{180}$

  $\Rightarrow C={20}^{0}C$

  $\frac{{}^{0}C}{100}=\frac{90-32}{180}$

  $\Rightarrow C={50}^{0}C$

  $\frac{{177}^{0}C}{100}=\frac{F-32}{180}\Rightarrow F={350.6}^{0}F$

With the calculated values the complete table is shown below:

C	17.780	-100	100	200	5080	1770
F	00	140	320	680	900	350.60

Conclusion:

The complete table is

C	17.780	-100	100	200	5080	1770
F	00	140	320	680	900	350.60