wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

We know that, for an ideal monoatomic gas, the total internal energy is a result of the translational kinetic energy only. For the oxygen molecule O2 (assume it doesn't oscillate along the bond axis), which rotates as well as translates, choose the correct statement(s) from the following


A

Change in translational kinetic energy of a sample of n moles = nCVΔT

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

Translational kinetic energy < rotational kinetic energy

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Translational kinetic energy > rotational kinetic energy
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Translational kinetic energy = rotational kinetic energy.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C Translational kinetic energy > rotational kinetic energy

The equipartition theorem postulates - each degree of freedom contributes an energy equal to (12)kT to the total internal energy of a molecule, depending on the temperature T. Let's count the number of degrees of freedom for an O2 molecule.

(1) Possible directions of translational motion are the three axes, x, y and z. Thus, number of translational degrees of motion = 3.

(2) Given the negligible size of the atoms, rotation about the bond-axis will not be significant. It can only rotate about the two axes shown (perpendicular to the bond-axis). Thus number of rotational degrees of motion = 2.

Therefore, according the equipartition theorem,

(i) Translational Kinetic energy, KTr = 32kT,

(ii) Rotational Kinetic energy, KRot = kT.

Clearly, KTr > KRot.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Theory of Equipartitions of Energy
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon