Q2DQ - University Physics with Modern Physics

Question

 If you heat the air inside a rigid, sealed container until its Kelvin temperature doubles, the air pressure in the container will also double. Is the same thing true if you double the Celsius temperature of the air in the container? Explain.

Step-by-Step Solution

Answer

If we double the Kelvin scale value, then the Celsius scale values does not double up.

Step 1: Relation between Kelvin scale and Celsius scale

The relation between Kelvin scale and Celsius scale is ${\mathrm{T}}_{\mathrm{k}}={\mathrm{T}}_{\mathrm{c}}+273$.

Step 2: Double both the Kelvin and Celsius values

Consider ${\mathrm{T}}_{\mathrm{k}}=100\mathrm{K}$. The Celsius scale will become

$$\begin{gathered} {\mathrm{T}}_{\mathrm{c}}=100-273 \\ {\mathrm{T}}_{\mathrm{c}}={173}^{°}\mathrm{C} \end{gathered}$$

Now, double the kelvin scale value. We will get ${\mathrm{T}}_{\mathrm{k}}=200\mathrm{K}$. The Celsius scale value will be

$$\begin{gathered} {\mathrm{T}}_{\mathrm{c}}=200-273 \\ {\mathrm{T}}_{\mathrm{c}}=-{73}^{°}\mathrm{C} \end{gathered}$$

Clearly, $-{73}^{°}\mathrm{C}$ is not the double of $-{173}^{°}\mathrm{C}$.

Hence, if we double the Kelvin scale value, then the Celsius scale values does not double up.