when temperature and pressure proportional to each other why viscosity is indirectly and directly pro. to that

Question

when temperature and pressure are proportional to each other why viscosity is indirectly and directly proportional to temperature and pressure?

Answer 1

The T and P proportionality comes from the ideal gas law PV=NRT, and is true only when V, N and R are held constant and no heat flows in or out of the gas after the change in T. Viscosity is an unrelated property and not part of the ideal gas law.

Answer 2

For the ideal gas, we can write PV = nRT = kT; where k is a case specific constant of proportionality. T is temperature in Kelvin and it is proportional to the mean average kinetic energy of the ideal gas molecule. In math talk, we can write T = KW; where W is the root mean square average of all the molecular speeds w. So we can rewrite the ideal gas law as: PV = kT = kKW As you can plainly see, when holding the volume V constant, an increase in pressure P will increase the temperature T, which is manifest by the increase in the mean average speeds of the ideal gas molecules. And there you are; the molecules are restricted in their motions by the constant volume. But the temperature remains proportional, not inversely so, to the applied pressure. You are incorrect.