Hello, Please i have a question about the internal energy: The Internal Kinetic energy is the motion of molecules and it's a random motion. But at macroscopic level the whole object formed by those molecules move in a same direction? how it can be? In a flowing fluid not static? thank you
In a solid object, the molecular movement isn't completely random; it's more as if the atoms are vibrating back and forth while keeping more or less the same general position relative to one another. If you want an analogy, imagine a bus full of unruly small children - the children may be in continuous random motion, but the ensemble of bus and brats is still moving steadily down the road. Even in a gas or a liquid, it is possible that all the molecules have the same average velocity over time, even though at any given moment many of them will have small random deviations from that average.
Thank you. So when we say that the internal energy is related to the microscopic kinetic energy what is the velocity taken here?
Imagine an observer moving at the same speed as the object; as far as that observer is concerned, the object is at rest, the time-averaged speed of each molecule in the object is zero, and the object has zero kinetic energy. Now the random molecular movement is the only movement, so all of the kinetic energy from all of that movement is counted as internal energy.
Another way to put it is to imagine an observer from whose point of view the total momentum of the molecules is zero. That is, the molecules are flying around in random directions so that their momenta cancel out completely when you add them together. According to that observer, the total KE is the "internal KE."
Jtbell is correct - that's a precise formulation of the fuzzy notion of "at rest relative to the object".
Just to see if i understand. If the fluid has a velocity of 5m/s for example then its molecules has an average of 5m/s. the internal kinetic energy is calculated by imagining an object that has the same velocity of the fluid and the molecules' velocity are related to 5m/s ?
Just a Last question please. In a flow of a fluid the temperature is related to the microscopic kinetic energy or to its macroscopic? And is there a dependency between the internal and macroscopic kinetic energy? or in another way: if a fluid is static and has a temperature of 18^{o}C then its internal kinetic energy is equal to 3/2KT. But when this fluid flows lets say it has the same temperature (18^{o}C) so it has the same internal kinetic energy as the static one but how come the average velocity(macroscopic) is not 0?
The temperature of a fluid depends on the motion of individual molecules relative to one another (or to their center of mass). I think that is what you mean by "microscopic". When you say "the average velocity (macroscopic)" that must be given relative to some external frame of reference. The temperature of a fluid is NOT relative to an external frame of reference and so cannot be dependent on the "macroscopic" motion or energy.