Question

The absolute temperature of an ideal diatomic gas is quadrupled what happens to the average speed of molecules

Answer 1

Answer:

here is your answer dear

Explanation:

Suppose the absolute temperature of an ideal gas is doubled from 100 K to 200 K.

(a) Does the average speed of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2?

(b) Choose the best explanation from among the following:

I. Doubling the Kelvin temperature doubles the average kinetic energy, but this implies an increase in the average speed by a factor of (2 = 1.414….., which is less than 2.

Answer 2

If the absolute temperature of an ideal diatomic gas is quadrupled, then, the average speed of the molecules is doubled.

Explanation:

• Consider a container, filled with ideal gas as shown in the figure.
• In this model, at a temperature $T$, each molecule possesses some speed.
• The mean of the speeds of all molecules is called the average speed of gas at temperature $T$.
• As temperature increases, the average speed increases.
• From Maxwell-Boltzmann statistical theory the average speed of molecules of an ideal gas at the temperature $T$ is given as:

        ${v_{avg}} = \sqrt {\frac{{8kT}}{{\pi m}}}$

• Here, $m$ is the mass of molecules and $k$ is Boltzmann constant. Now if the temperature from $T$ becomes $4T$, then,

       $\begin{gathered} {V_{avg}} = \sqrt {\frac{{8k \times 4T}}{{\pi m}}} \hfill \\ {V_{avg}} = 2\sqrt {\frac{{8kT}}{{\pi m}}} \hfill \\ {V_{avg}} = 2{v_{avg}} \hfill \\ \end{gathered}$

• Hence, if the absolute temperature of an ideal diatomic gas is quadrupled, then, the average speed of molecules is doubled.

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