InterviewSolution
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InterviewSolution
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One mole of an ideak gas consisting of monatomic molecules is enclosed in a vessel at a temperature `T_0 = 300 K`. How many times and in what way will the statistical weight of this system (gas) vary if it heated isochorically by `Delta T = 1.0 K` ? |
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Answer» For a monoatomic gas `C_V = (3)/(2) R` per mole The entropy change in the process is `Delta S = S - S_0 = int_(T_0)^(T_0 + Delta T) C_V (dT)/(T) = (3)/(2) R 1n (1 + (Delta T)/(T_0))` N ow from the Boltzmann equation `S = k 1n Omega` `(Omega)/(Omega_0) = e^((S - S_0)//k) = (1 + (Delta T)/(T_0))^((3 N_A)/(2)) = (1 + (1)/(300))^((3 xx 6)/(2) xx 10^23) = 10^23 xx 10^21` Thus the statistical weight increases by this factor. |
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