Chapter 20: Q. 19 (page 567)

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

Short Answer

Expert verified

The $r m s$ speed on the temperature is $2.12$

Step by step solution

Explanation

Let us remember that the formula giving the dependence of the $r m s$ speed on the temperature is

localid="1648397843905" $v_{r m s} = \sqrt{\frac{3 k_{B} T}{m}} = C \sqrt{T}$

where $C$ is a constant. Therefore, considering two $r m s$ speeds and $v_{1}$ $v_{2}$ , we have

$\frac{v_{2}}{v_{1}} = \frac{C \sqrt{T_{2}}}{C \sqrt{T_{1}}} = \sqrt{\frac{T_{2}}{T_{1}}}$

The rate of temperature

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

Substitute the value in formula

$\frac{v_{2}}{v_{1}} = \sqrt{\frac{1273}{283}}$

$= 2.12$

The heat is moving at a rate of $2.12$

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

Short Answer

Step by step solution

Explanation

The rate of temperature

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

Short Answer

Step by step solution

Explanation

The rate of temperature

One App. One Place for Learning.

Most popular questions from this chapter

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