The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is :

 

❓ Question

The helium and argon gases are placed in a flask at the same room temperature (300 K).
What is the ratio of their average kinetic energies (per molecule)?

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🖼️ Question Image

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✍️ Short Solution

Step 1 — Recall the formula for average kinetic energy per molecule

For any gas, according to the kinetic theory of gases, the average kinetic energy of a molecule is:

$$\overline{E_k}=\frac{3}{2}kT$$

where

• $k$ = Boltzmann constant (1.38 × 10⁻²³ J/K)

• $T$ = absolute temperature in kelvin

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Step 2 — Dependence on temperature

Notice that the average kinetic energy per molecule depends only on temperature, not on the nature (mass or type) of the gas.

That means — if two gases are at the same temperature, each molecule has the same average kinetic energy regardless of whether the gas is light (like helium) or heavy (like argon).

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Step 3 — Apply given data

Given:

• $T_{\text{He}} = T_{\text{Ar}} = 300~\text{K}$
  

So,

$$E_{\text{He}}=\frac{3}{2}k{T}_{\text{He}},E_{\text{Ar}}=\frac{3}{2}k{T}_{\text{Ar}}$$

Taking their ratio:

$$\frac{E_{\text{He}}}{E_{\text{Ar}}}=\frac{\frac{3}{2}k{T}_{\text{He}}}{\frac{3}{2}k{T}_{\text{Ar}}}=\frac{T_{\text{He}}}{T_{\text{Ar}}}=\frac{300}{300}=1.$$

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🧮 Image Solution

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✅ Conclusion & Video Solution

✅ Final Answer:

$$\boxed{{\displaystyle \frac{E_{\text{He}}}{E_{\text{Ar}}}=1:\mathrm{1}}}$$

Concept Recap:

• The average kinetic energy per molecule depends only on absolute temperature.

• It is independent of molecular mass or type of gas.

• So, all gases at the same temperature have the same average energy per molecule, though their speeds differ (lighter gases move faster).