3. [1] Show that the entropy of an ideal gas can be represented as V (STD)) S = NkB In (3.4) where g is an unknown funct

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3 1 Show That The Entropy Of An Ideal Gas Can Be Represented As V Std S Nkb In 3 4 Where G Is An Unknown Funct 1 (88.63 KiB) Viewed 12 times

3. [1] Show that the entropy of an ideal gas can be represented as V (STD)) S = NkB In (3.4) where g is an unknown function of T. Hint: You can start off with the Maxwell relation for (V) N.T 4. [3] Derive a general formula for the entropy of a non-ideal gas using the Virial expansion (up to the p² term). Show that the entropy correction factors for both the hard-sphere and square-well potential converge to the same value when & << KBT. 5. [3] Consider the van der Waals equation of state. In the limit of low density, calculate the values of B₁ (T), B₂(T), and B³(T) and relate them back to the hard-sphere and square-well potentials. What do you notice about all Virial coefficients B3(T) onwards in terms of their dependence on the excluded volume?