Question

Two gases A and B are at absolute temperatures 350 K and 420 K respectively. The ratio of average kinetic energy of the molecules of gas B to that of gas A is

• A. $6 : 5$
• B. $\sqrt{6} : \sqrt{5}$
• C. $36 : 25$
• D. $5 : 6$

Hint:

Kinetic energy depends only on temperature, not on the mass or nature of the gas molecules.

Answer 1

The Correct Option is A

Step 1: Concept
The average kinetic energy of gas molecules is directly proportional to the absolute temperature ($KE_{avg} = \frac{3}{2} k_B T$).

Step 2: Meaning
Since $KE \propto T$, the ratio of kinetic energies is equal to the ratio of their absolute temperatures.

Step 3: Analysis
Ratio $= \frac{KE_B}{KE_A} = \frac{T_B}{T_A} = \frac{420}{350}$. Simplifying the fraction by dividing by 70 gives $\frac{6}{5}$.

Step 4: Conclusion
The ratio of average kinetic energy of gas B to gas A is $6:5$. Final Answer: (A)