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Viscosity:

In gasses, forces between atoms are not important and the transfer of momentum (hence force, hence viscosity) between different adjacent regions of a fluid is due to the movement of particles over long distance. Higher temperature means faster movement means higher viscosity in a gas.

In liquids, forces between particles dominate and shear force is transmitted through those interactions with adjacent particles. Higher temperature means more short distance particle movement and more varied interaction with neighboring particles thus decreasing the effectiveness of transmitting shear force and decreasing viscosity.

(These trends in viscosity are only general and complex interactions of particles can produce different results than described here.)

Density:

If the pressure is held constant, an increase in temperature normally results in an increase in volume of a liquid, solid or gas. This parallels the explanation of how particle motion at the microscopic level produces pressure by collisions with the walls of the containing volume. More temperature means more energetic particles that have more momentum to transfer to container walls. With constant pressure, the walls expand.

(The obvious caveat here is that molecular orientations and molecular forces can be complex and this connection between increased temperature and decrease density is not universally true. The properties of water between 0 Celsius and 4 Celsius are a well known counter example to the general rule.)

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