Question

$C=\frac{5}{9}(F-32)$
The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of $1$ degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius.
II. A temperature increase of $1$ degree Celsius is equivalent to a temperature increase of $1.8$ degrees Fahrenheit.
III. A temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of $1$ degree Celsius

• A. I only
• B. II only
• C. III only
• D. I and II only

Answer 1

Answer: (D)

I and II only

Given:- $C=\frac{5}{9}(F-32)$

$\Rightarrow F=\frac{9}{5}C+32$

(I) If F' = F + 1

$C^{\prime }=\frac{5}{9}(F^{\prime }-32)$

$C^{\prime }=\frac{5}{9}(F+1-32)$

$C^{\prime }=\frac{5}{9}(F-32)+\frac{5}{9}\times 1$

$C^{\prime }=C+\frac{5}{9}$

Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius.

Therefore, statement I is true.

(II) If C' = C + 1

$F^{\prime }=\frac{9}{5}{C}^{\prime }+32$

$F^{\prime }=\frac{9}{5}(C+1)+32$

$F^{\prime }=(\frac{9}{5}C+32)+\frac{9}{5}$

$F^{\prime }=F+\frac{9}{5}$

$F^{\prime }=F+1.8$

Hence, a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

Therefore, statement II is true.

(III) If $F^{\prime }=F+\frac{5}{9}$

$C^{\prime }=\frac{5}{9}(F^{\prime }-32)$

$C^{\prime }=\frac{5}{9}(F+\frac{5}{9}-32)$

$C^{\prime }=\frac{5}{9}(F-32)+\frac{5}{9}\times \frac{5}{9}$

$C^{\prime }=C+\frac{25}{81}$

Hence, a temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of $\frac{25}{81}$ degree Celsius.

Therefore, statement III is false.