Question

By what factor does the $rms$speed of a molecule change if the temperature is increased from $10°C$ to $1000°C$?

Short answer

The$rms$speed on the temperature is$2.12$

Step-by-step solution

Explanation 

Let us remember that the formula giving the dependence of the $rms$speed on the temperature is

localid="1648397843905" $$\begin{gathered} v_{rms}=\sqrt{\frac{3k_{B}T}{m}} \\ =C\sqrt{T} \end{gathered}$$

where $C$is a constant. Therefore, considering two$rms$ speeds and $v_1$$v_2$, we have

$$\begin{gathered} \frac{v_2}{v_1}=\frac{C\sqrt{T_2}}{C\sqrt{T_1}} \\ =\sqrt{\frac{T_2}{T_1}} \end{gathered}$$

The rate of temperature

Keep in mind that the temperatures must be expressed in degrees Kelvin, which means that they must be $10+273=283K$and $1000+273=1273K$

Substitute the value in formula

$\frac{v_2}{v_1}=\sqrt{\frac{1273}{283}}$

$=2.12$

The heat is moving at a rate of $2.12$