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Question: The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K a...

The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are 6.21×10−21J6.21 \times 10^{- 21}J and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)

A

12.42×10−21J,968m/s12.42 \times 10^{- 21}J,968m/s

B

8.78×10−21J,684m/s8.78 \times 10^{- 21}J,684m/s

C

6.21×10−21J,968m/s6.21 \times 10^{- 21}J,968m/s

D

12.42×10−21J,684m/s12.42 \times 10^{- 21}J,684m/s

Answer

12.42×10−21J,684m/s12.42 \times 10^{- 21}J,684m/s

Explanation

Solution

E∝TE \propto T but vrms∝Tv_{rms} \propto \sqrt{T}

i.e. if temperature becomes twice then energy will becomes two time i.e. 2 × 6.21 × 10–21 = 12.42 × 10–21 J

But rms speed will become 2\sqrt{2} times i.e. 484×2=684m⥂/⥂s484 \times \sqrt{2} = 684m ⥂ / ⥂ s.