1) For a micro-canonical ensemble, with N microstates all at energy E, what is the probability of any given microstate occuring?
2)For the canonical ensemble write down the probability distribution function for a system, at energy E, in thermal equilibrium with its surroundings.
3)For the grand canonical ensemble write down the probability distribution function for a system, at energy E with N particles, in equilibrium with its surroundings.
4)
i) Write down the master equation for the internal energy in thermodynamics. Explain how this follows from the laws of thermodynamics.
ii) use two legendre transformations to yield a master equation for the grand potential.
iii) derive the integral form of the master equation from i) and ii). (do not assume the euler equation). Derive the intergral form given that the differential master equation is an euler relation.
Please give a detailed description.
2)For the canonical ensemble write down the probability distribution function for a system, at energy E, in thermal equilibrium with its surroundings.
3)For the grand canonical ensemble write down the probability distribution function for a system, at energy E with N particles, in equilibrium with its surroundings.
4)
i) Write down the master equation for the internal energy in thermodynamics. Explain how this follows from the laws of thermodynamics.
ii) use two legendre transformations to yield a master equation for the grand potential.
iii) derive the integral form of the master equation from i) and ii). (do not assume the euler equation). Derive the intergral form given that the differential master equation is an euler relation.
Please give a detailed description.