Average Kinetic Energy of Gases at Same Temperature

 

❓ 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

✍️ Short Explanation

This problem is based on:

👉 Kinetic theory of gases
👉 Average kinetic energy
👉 Temperature dependence.

Main idea:

Average kinetic energy per molecule depends only on temperature.

$$\boxed{ \text{Average KE}=\frac32kT }$$

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🔷 Step 1 — Write Average KE Formula 💯

For any gas molecule:

$$\boxed{ \text{Average KE}=\frac32kT }$$

where:

• $k$ = Boltzmann constant
• $T$ = absolute temperature

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🔷 Step 2 — Compare Helium and Argon

Both gases are at same temperature:

$$T=300\text{ K}$$

Thus:

$$\text{KE}_{He} = \frac32kT$$

and:

$$\text{KE}_{Ar} = \frac32kT$$

Therefore:

$$\boxed{ \text{KE}_{He}:\text{KE}_{Ar}=1:1 }$$

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🔷 Step 3 — Important Observation

Average kinetic energy:

✔ Depends only on temperature

❌ Does NOT depend on mass

❌ Does NOT depend on molar mass

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🔷 Step 4 — JEE Trap Alert 🚨

❌ Molar masses $4$ and $40$ use kar lena unnecessarily

❌ RMS speed aur kinetic energy confuse kar dena

Remember:

RMS speed depends on mass

but:

$$\boxed{ \text{Average KE depends only on temperature} }$$

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✅ Final Answer

$$\boxed{ 1:1 }$$

(Option 3)

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