| A fixed container is fitted with a piston which is attached to a spring of spring constant k. The other end of the spring is attached to a rigid wall. Initially the spring is in its natural length and the length of container between the piston and its side wall is L. Now an ideal diatomic gas is slowly filled in the container so that the piston moves quasistatically. If pushed the piston by x so that the spring now is compressed by x. The total rotational kinetic energy of the gas molecules in terms of the displacement x of the piston is (there is vacuum outside the container) |
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A) \[kxL\]
B) \[4kxL\]
C) \[kx\,(x+L)\]
D) \[\frac{2k{{x}^{2}}}{L}\]
Correct Answer: C
Solution :
[C]| Rotational K.E. = Rotational degree of freedom \[\times \,\,\frac{1}{2}\,\,nRT\] |
| \[=2\times \frac{1}{2}\,\,nRT=nRT=PV\] |
| \[PA.\frac{V}{A}\]=force on piston \[(L+x)\] |
| \[=\,\,\,kx\,\,\,(L+x)\] |
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