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1. Calculate the molar entropy of a rubber. 2. Calculate the temperature dependence of a rubber elastic constant. 3. Calculate the difference in the molar heat capacities of stretched and unstretched rubber. Solution: 1. The entropy, S, is obtained from the Boltzmann equation, i.e. S=kBG2S=kBGS=kBlnGS=kBG1S=kBexpG difference between Nand N+is denoted by n=NN+&N, and can be obtained from the chain's geometry, viz., nnnnn2+020N02020N0+00 G=G(N+,N)G(N,N+), by using combinatorics one can state that GGGGG=(N++N)!(N+N)!=N!N+!=(N++N)!N+!N!=N!N!=N+!N!(N++N)