@jcsd. That's clear. But you use the term "Rank" in a different way than for example, this paper: http://www.its.caltech.edu/~matilde/WeitzMa10Abstract.pdf. If we assume that rank is defined as it is in this paper, then can you still say it doesn't change as you move from point to point...
Tensors can be of type (n, m), denoting n covariant and m contravariant indicies. Rank is a concept that comes from matrix rank and is basically the number of "simple" terms it takes to write out a tensor. Sometimes, however, I recall seeing or hearing things like "the metric tensor is a rank 2...
Hmmm ... I am thinking it's the other way around. Metal, due to free electrons, conducts heat better than plastic. So heat will flow from your hand into the steal at a greater rate than it will from your hand to to the plastic.
Yes, if you are restrict yourself to adiabatic paths, then the work form can be written as the dw, where w is a function of thermodynamic variables.
This means the work done will only depend on the endpoints of the path -- as long as we are only considering paths along which dq = 0.
Yes, never assumed it was an isolated system. But you are right.
He uses the Virial Theorem to show that, under certain conditions, the total energy is equal to minus the kinetic energy or equal to the one-half the potential energy. This means the rate of change of kinetic energy with...
See: http://math.ucr.edu/home/baez/entropy.html for the source of the question. Baez show that the the decrease in potential energy is greater than the increase in kinetic energy: overall the internal energy decreases.
This is an ideal* gas in which particles are pointlike. We don't have em...
A gas cloud shrinks due to gravitational forces. The gas gets hotter because the velocity (hence kinetic energy) of the gas particles gets larger. At the same time the potential energy gets smaller because the gas particles are closer to each other.
Once you get past the fact that the...