Question

Using statistical thermodynamics and considering only translational and rotational motions prove that for the nonlinear molecule U=U(0) +3RT

Please show work!!

Answer 1

U = U (0) + 3RT (nonlinear molecule, translation and rotation only) mm .The internal energy increases twice as quickly with temperature compared .The internal energy of relating molecules in reduced phases also has a contribution from the potential energy of their interaction.

However, the crucial molecular point is that, as the temperature of a system is raised, the internal energy increases as the various modes of motion become more highly excited.

It has been found experimentally that the internal energy of a system may be changed either by doing work on the system or by heating it. But we know how the energy transfer has occurred (because we can see if a weight has been raised or lowered in the surroundings, indicating transfer of energy by doing work, or if ice has melted in the surroundings, indicating transfer of energy as heat), the system is blind to the mode employed. Heat and work are equal ways of changing a system's internal energy.

A system is like a bank: it accepts deposits in either currency, but stores its reserves as internal energy. It is found experimentally that, if a system is inaccessible from its surroundings, then no change in internal energy takes place.

This summary of observations is now known as the First Law of thermodynamics and expressed as follows: The internal energy of an isolated system is constant.