Now if epsilon_0 = 2kcal mol^-1 and gamma = 1000, find the temperature T_0 at wh

Question

Now if epsilon_0 = 2kcal mol^-1 and gamma = 1000, find the temperature T_0 at which p_1 = p_3. Under condition (d), compute p*_1, p*_2, and p*_3 at temperature T_0. The speed of sound in air is approximately the average velocity (v_x^2)^1/2 of the gas molecules. Compute this speed for T = 0 degree C, assuming that air is mostly nitrogen gas. The properties of a two-state system. Given a two-state system in which the low energy level is 600 cal mol^-1, the high energy level is 1800 cal mol^-1, and the temperature of the system is 300 K, What is the partition function q? What is the average energy (epsilon)? Consider a particle that has two states: bonded to a surface, or non-bonded (released).

Explanation / Answer

a.) q = e^-((E1 + E2)/kT))

where k is boltmann constant

.6 kcal = 2510.4 J

1.8 kcal = 7531.2

q = e^ -(10041.6/(1.38064852 × 10-23 * 300 ))

b.) Average Energy = = PJ EJ

= [2510.4 * e^ -(2510.4/(1.38064852 × 10-23 * 300 )) + 7531.2 * e^ -(7531.2/(1.38064852 × 10-23 * 300 )) ] / [e^ -(2510.4/(1.38064852 × 10-23 * 300 )) + e^ -(7531.2/(1.38064852 × 10-23 * 300 ))]

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