Thermodynamics: Gas

The Hydrogen atom consists of an electron and a proton, so the total spin is 1. Therefore, the Hydrogen atom is a boson.

Recall that the chemical potential for an ideal gas is μ = τlog . Remember that an ideal gas must have n n _Q . Therefore, 1 . The log of a number between 0 and 1 is negative, and the temperature for any ideal gas must be positive. Therefore, the chemical potential μ is negative for an ideal gas. The equation breaks down as n→n _Q , for we are leaving the classical regime and μ→ 0 .

This problem tests whether you remember all of the conversions between fundamental and conventional units, and tests whether you can recall the equation we derived for the energy of an ideal gas. Recall that U = Nτ . N here will be Avogadro's Number, which is 6.02×10²³ . Room temperature is 25 ^o C , which is 298K . Therefore τ = 298k _B . The final result gives us U = 2477 Joules.

Recall that σ = N log + . Now = 100 . Remembering that log refers to ln, we solve to find that σ = 4.28×10²⁴ . Notice that as n gets smaller, the entropy gets bigger. You can imagine that a gas with more room to move around per particle would have more randomness then one in which the particles were forced together in a small space.

We recall that C _V = N and C _p = N . Therefore, C _V = 9.03×10²³ and C _p = 1.51×10²⁴ .