Question

18-14. There is a mathematical procedure to calculate the error in replacing a summation by an integral as we do for the translational and rotational partition functions. The formula is called the Euler-Maclaurin summation formula and goes as follows: f(n) = âˆ‘[f(n)dn] + âˆ«[f(u)du] + 1/2[f(a) + f(b)] - 1/12[f'(a) - f'(b)] + 1/720[f'''(a) + f'''(b)]dn Apply this formula to Equation 18.33 to obtain Î¶ro (T) = 1 + [Î£(Fn) + 1/2(F0 + F7) + 1/12(F'(0) - F'(7)) + 1/720(F'''(0) + F'''(7))]dn Calculate the correction to replacing Equation 18.33 by an integral for NÎ¶(g) at 300 K; Î—Î¶(g) at 300 K (being so light, H is an extreme example)

          18-14. There is a mathematical procedure to calculate the error in replacing a summation by an integral as we do for the translational and rotational partition functions. The formula is called the Euler-Maclaurin summation formula and goes as follows:
f(n) = âˆ‘[f(n)dn] + âˆ«[f(u)du] + 1/2[f(a) + f(b)] - 1/12[f'(a) - f'(b)] + 1/720[f'''(a) + f'''(b)]dn
Apply this formula to Equation 18.33 to obtain Î¶ro (T) = 1 + [Î£(Fn) + 1/2(F0 + F7) + 1/12(F'(0) - F'(7)) + 1/720(F'''(0) + F'''(7))]dn
Calculate the correction to replacing Equation 18.33 by an integral for NÎ¶(g) at 300 K; Î—Î¶(g) at 300 K (being so light, H is an extreme example)

18 14 there is a mathematical procedure to calculate the error in replacing a summation by an integral as we do for the translational and rotational partition functions the formula is called 95947

Added by Charles E.

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