Question

You put a bottle of soft drink in refrigerator and leave it until its temperature has dropped $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{K}$.What is its temperature change in (a) F° and (b) C°?

Short answer

The temperature change in degree Celsius is $-10°\mathrm{C}$ .

Given:

The temperature change in Kelvin is $∆{\mathrm{T}}_{\mathrm{K}}=10.0\mathrm{K}$.

Step-by-step solution

Step 1: Conversion of temperature from Kelvin to Celsius 

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

${\mathrm{T}}_{\mathrm{C}}={\mathrm{T}}_{\mathrm{K}}-273.15$

Where is the ${\mathrm{T}}_{\mathrm{C}}$ temperature in Celsius scale ${\mathrm{T}}_{\mathrm{K}}$temperature in Kelvin scale .

Conversion of change in temperature in degree Celsius to Kelvin

$$\begin{gathered} {\mathrm{T}}_{\mathrm{Cf}}={\mathrm{T}}_{\mathrm{Ci}}={\mathrm{T}}_{\mathrm{Kf}}-273.15-\left({\mathrm{T}}_{\mathrm{Ki}}-273.15\right) \\ ∆{\mathrm{T}}_{\mathrm{C}}=∆{\mathrm{T}}_{\mathrm{K}} \end{gathered}$$

Where,

${\mathrm{T}}_{\mathrm{Cf}},{\mathrm{T}}_{\mathrm{Ci}}$ and ${\mathrm{T}}_{\mathrm{Kf}},{\mathrm{T}}_{\mathrm{Ki}}$final and initial temperatures in Celsius scale and Kelvin scale respectively .

$∆{\mathrm{T}}_{\mathrm{C}}$and $∆{\mathrm{T}}_{\mathrm{K}}$are change in temperature on Celsius and Kelvin scale respectively.

Calculation of change in temperature on degree Celsius scale

Using relation

$∆{\mathrm{T}}_{\mathrm{C}}=-∆{\mathrm{T}}_{\mathrm{K}}$

Now, putting the value in above equation

$$\begin{gathered} ∆{\mathrm{T}}_{\mathrm{C}}=-\left(10\right) \\ ∆{\mathrm{T}}_{\mathrm{C}}=-10°\mathrm{C} \end{gathered}$$

Thus, the temperature change in degree Celsius is $-10°\mathrm{C}$.