[Four-digit Integer] The second virial coefficient of methane can be approximate by the empirical equation: B = a + b × e^-c/T^2, where a = -0.2 bar^-1, b = 0.22 bar^-1, and c = 950 K^2. What is the v

Question

[Four-digit Integer] The second virial coefficient of methane can be approximate by the empirical equation: B = a + b × e^-c/T^2, where a = -0.2 bar^-1, b = 0.22 bar^-1, and c = 950 K^2. What is the value of the Boyle temperature of methane (in K)? (ln 1.1 = 0.095)

Prashant Kotian · Accepted Answer

Correct answer: 0100. At Boyle's temperature T_B, the second virial coefficient B is equal to zero: B = 0 → a + b × e^-c/T_B^2 = 0 → -0.2 + 0.22 × e^-950/T_B^2 = 0 → e^-950/T_B^2 = 0.2 / 0.22 = 1 / 1.1. Taking natural log: -950 / T_B^2 = ln(1 / 1.1) = -ln(1.1) = -0.095 → T_B^2 = 950 / 0.095 = 10,000 → T_B = 100 K. Thus, the 4-digit answer is 0100.

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