Question

$1^\circ C$ rise in temperature is equal to the rise of:
A. $1^\circ F$
B. $9/5^\circ F$
C. $5/9^\circ F$
D. $33^\circ F$

Answer 1

Hint: The temperature of any substance or solution is given in terms of degree Celsius and degree Fahrenheit. The linear equation $F = \dfrac{9}{5}C + 32$ gives the relation between temperature present in degree Fahrenheit and the temperature present in degree celsius.

Complete step by step answer:
The two scales to measure the temperature is Fahrenheit and Celsius. The temperature which is shown by the centigrade scale is in terms of degree Celsius and the temperature which is shown by the Fahrenheit scale is in terms of degree Fahrenheit.
The linear equation to convert temperature in Celsius into temperature in Fahrenheit is shown below.
$F = \dfrac{9}{5}C + 32$……..(1)
Where,
F is Fahrenheit
C is Celsius.
It is given that the temperature rises by $1^\circ C$, therefore the new temperature in degree celsius is given as shown below.
$C' = C + 1$
Where,
C’ is the new temperature in degrees Celsius.
The linear equation for new temperature in Fahrenheit is shown below.
$F' = \dfrac{9}{5}C + 32$………(2)
F’ is the new temperature in Fahrenheit.
Substitute the value of C’ in the above equation as shown below.
$\Rightarrow F' = \dfrac{9}{5}(C + 1) + 32$
Equate the above given expression.
$\Rightarrow F' = \dfrac{9}{5}C + \dfrac{9}{5} + 32$
$\Rightarrow F' = \left( {\dfrac{9}{5}C + 32} \right) + \dfrac{9}{5}$
$\Rightarrow F' = F + \dfrac{9}{5}$ (from equation 1)
Thus, $1^\circ C$ rise in temperature is equal to the rise of $9/5^\circ F$.
So, the correct answer is “Option B”.

Note:
 The relation between the degree Celsius and degree Fahrenheit is proportional to each other. The linear equation for the conversion of Fahrenheit to Celsius is shown below.
$C = \dfrac{5}{9}(F - 32)$.
Both the temperature show different freezing point values of water and both have variation in their unit between each temperature scale.