In classical thermodynamics the (non-normalized) probability for a single particle amongst a large number of identical particles to have an energy e is given by p(e) = exp(− e kbt ). suppose the energy of the particles in question takes the form e = ax2 , where a is a positive constant, and x is a variable ranging (in whatever units are appropriate) from zero to infinity. show that the average energy for this system is given by hei = kbt 2 . this is known as the equipartition theorem.

What is the scientific definition of energy that relates to work

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.

Which is not an example of how an object gains elastic potential energy by stretching? a. jumping on a pogo stick b. pulling on a rubber band c. jumping on a trampoline