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quiz3b_solutions

quiz3b_solutions - process since the system returns to the...

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Name________________________________________________ In Section Quiz 3B (11 09 05, Aathavan) 1. A system has its entropy related to its total energy by the following relationship. S = c U 2 , where c is a constant. What is the C v of this system? (5) Solution: cU dU dS T 2 1 = = 2 2 1 2 1 cT cT dT d dT dU C v - = = = (Note: This system has negative heat capacity ( the system cools down when you add energy) which is not very intuitive. There are some systems where such a behavior is known http://www.aip.org/pnu/2001/split/524-2.html Note also that for an ideal gas S=c lnU (try to prove this for an exercise!) and any system that has entropy increasing faster with energy than will end up with a negative heat capacity.) 2 Consider a cyclic process involving a gas. If the pressure of the gas varies during the process but returns to the original value at the end, is it correct to write ΔH = q process ? Explain (2) Solution: Enthalpy is a state function and heat transfer is a path function. In a cyclic

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Unformatted text preview: process, since the system returns to the same state ΔH=0, but q need not be 0. More generally while dH=dq, but 1 2 2 1 H H dH H-= = ∆ ∫ (state function) 1 2 2 1 q q dq q-≠ = ∫ (path function) 3. The system below has infinite number of equally spaced energy levels. There are two possible states for every energy level. What will be the multiplicity of the system if the total energy, U=ne and there are two particles in the system (3) .......................................... 5e_________ _________ 4e_________ _________ 3e_________ _________ 2e_________ _________ e_________ _________ 0_________ _________ Solution: W = W positional X W energy W energy = (n+1) (There are n+1 ways of distributing n.e of energy between two particles in this system – see quiz 3A) W positional = 2 X 2 (Each particle can be in two equivalent positions.) =4 W = W positional X W energy =4(n+1)...
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