Question

The temperature in Browning ,Montana ,was $44.0°\mathrm{F}$on January $23,1916$.The next day the temperature plummeted to $-56°\mathrm{F}$. What was the temperature change in Celsius degrees?

Short answer

The change in temperature in degree Celsius is $-56°\mathrm{F}$

Given :

Initial temperature is ${\mathrm{T}}_{\mathrm{i}}=44.0°\mathrm{F}$.

Initial temperature is ${\mathrm{T}}_{\mathrm{f}}=-56°\mathrm{F}$

Step-by-step solution

To covert the temperature on Fahrenheit scale into Celsius scale.

Temperature in Fahrenheit scale can be converted in temperature in Celsius scale by formula:

${\mathrm{T}}_{\mathrm{c}}=\frac{5}{9}\left({\mathrm{T}}_{\mathrm{F}}-32\right)$

Where is the ${\mathrm{T}}_{\mathrm{F}}$temperature in Fahrenheit scale and ${\mathrm{T}}_{\mathrm{c}}$temperature in Celsius scale.

Calculation of initial temperature in Celsius scale.

Using formula

${\mathrm{T}}_{\mathrm{ci}}=\frac{5}{9}\left({\mathrm{T}}_{\mathrm{Fi}}-32\right)$

Where , ${\mathrm{T}}_{\mathrm{ci}}$is the initial temperature in Celsius scale and ${\mathrm{T}}_{\mathrm{Fi}}$is the initial temperature in Fahrenheit scale.

Now, putting the value of ${\mathrm{T}}_{\mathrm{Fi}}$in above equation

$$\begin{gathered} {\mathrm{T}}_{\mathrm{ci}}=\frac{5}{9}\left(44-32\right) \\ {\mathrm{T}}_{\mathrm{ci}}=\frac{5}{9}\left(12\right) \\ {\mathrm{T}}_{\mathrm{ci}}=6.7°\mathrm{C} \end{gathered}$$

Calculation of final temperature in Celsius scale

Using formula

${\mathrm{T}}_{\mathrm{cf}}=\frac{5}{9}\left({\mathrm{T}}_{\mathrm{Ff}}-32\right)$

Where ${\mathrm{T}}_{\mathrm{cf}}$ is the final temperature in Celsius scale and ${\mathrm{T}}_{\mathrm{Ff}}$is the final temperature in Fahrenheit scale.

Now putting the value of localid="1664352325685" ${\mathrm{T}}_{\mathrm{Ff}}$in above equation

$$\begin{gathered} {\mathrm{T}}_{\mathrm{Cf}}=\frac{5}{9}\left(-56-32\right) \\ {\mathrm{T}}_{\mathrm{Cf}}=\frac{5}{9}\times \left(-88\right) \\ {\mathrm{T}}_{\mathrm{Cf}}=-48.9°\mathrm{C} \end{gathered}$$

Calculation of change in temperature

Change in temperature $∆\mathrm{T}$is equals to the final temperature -- initial temperature

$$\begin{gathered} ∆\mathrm{T}={\mathrm{T}}_{\mathrm{Cf}}-{\mathrm{T}}_{\mathrm{Ci}} \\ ∆\mathrm{T}=-49.9-6.7 \\ ∆\mathrm{T}=-55.6°\mathrm{C} \end{gathered}$$

Thus, the change in temperature in degree Celsius is $-55.6°\mathrm{C}$