ThermodynamicsHard
Question
The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are 6.21 × 10-21 J and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)
Options
A.12.42 × 10-21 J, 968 m/s
B.8.78 × 10-21 J, 684 m/s
C.6.21 × 10-21 J, 968 m/s
D.12.42 × 10-21 J, 684 m/s
Solution
The average translation KE = 
kT which is directly proportional to T, while rms speed of molecules is given by
i.e., vrms 0 ∝ √T
When temperature of gas is increased from 300 K to 600 K (i.e., 2 times), the average translation KE will increase to 2 times and rms speed to √2 or 1.414 times.
∴ Average translational KE = 2 × 6.21 × 10-21 J
= 12.42 × 10-21 J
and vrms = (1.414) (484) m/s
684 m/s
kT which is directly proportional to T, while rms speed of molecules is given by i.e., vrms 0 ∝ √TWhen temperature of gas is increased from 300 K to 600 K (i.e., 2 times), the average translation KE will increase to 2 times and rms speed to √2 or 1.414 times.
∴ Average translational KE = 2 × 6.21 × 10-21 J
= 12.42 × 10-21 J
and vrms = (1.414) (484) m/s
684 m/sCreate a free account to view solution
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