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Molecular Chain (MIT, Princeton, Colorado)
Consider a one-dimensional chain consisting of N molecules which exist in two configurations, α, β, with corresponding energies and lengths α and β. The chain is focus to a tensile force f.
a) Write down the partition function ZN for the system.
b) Compute the average length (L) as a function f of and the temperature T.
c) Assume that anda>b. Evaluate the average length (L) in the absence of the tensile force f = 0 as a function of temperature. What are the high-temperature and low-temperature limits and what is the characteristic temperature at which the changeover between the two limits takes place?
d) Estimate the linear response function
Produce a universal argument to show that X>0.
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The devices in power system shown in Figure 2 have the following ratings: G1 : 100 MVA, 13.8 kV grounded Y, X” = 0.15 pu, X2 = 0.015 pu Xo = 0.05 pu G2 : 50 MVA, 20.0 kV grounded
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