Q²- A system of two energy levels E, and E₁ is populated by N particles at temperature T. The particlespopulate the energy levels according to the classical distribution law.(a) Derive an expression for the average energy per particle.(b) Compute the average energy per particle vs the temperature as T → 0 and T → co(c) Derive an expression for the specific heat of the system of N particles(d) Compute the specific heat in the limits T→ 0 and T → ∞o.

Answered: Image /qna-images/answer/d13e00f9-7b4c-455c-9699-e3e8886c801f.jpg

Answered: Q²- A system of two energy levels E,…

Similar questions

How to solve this question
The partition funetion for the ensemble characterized by constant V, E, and G = µÑ is given to a very good approximation by ø(V, E, µN)=Q(N,V,E)eBHN, where G = µN is the Gibbs energy (µ is the chemical potential and N is the average number of particles). Find an expression for the characteristic thermodynamic function for this ensemble in terms of the partition function ø(V, E, µN).
One-dimensional harmonic oscillators in equilibrium with a heat bath (a) Calculate the specific heat of the one-dimensional harmonic oscillator as a function of temperature (b) Plot the T -dependence of the mean energy per particle E/N and the specific heat c. Show that E/N → kT at high temperatures for which kT > hw In this limit the energy kT is large in comparison to hw , the separation between energy levels. Hint: expand the exponential function 1 ē = ħw + eBhw
Region 1 is x 0 with &2 = 460. If E2 = 6a - 10a, + 8a: V/m, (a) find P1, and P2, (b) calculate the energy densities in both regions.
how do I calculate an average energy when there are three psi unknowns? PSI= c1*psi1(x) + c2*psi2(x) + c3*psi3(x) also, how do I calculate probability when there is an energy given?
2) You are hiking along a trail in a wide, dry canyon where the outdoor temperature is T = 32° C. To determine how far you are away from the canyon wall you yell “Hello” and hear the echo t = 3.5 s later. Randomized Variables T = 32° C t = 3.5 s a) Calculate the speed of sound in the valley in meters per second, assuming the speed at 0° C is 330 m/s. b) How far are you from the canyon wall, in meters? c) If you stood at the same point on a cold morning where the temperature was T2 = -3.5 degrees C, how long would it have taken for you to hear the echo, in seconds?
The infinitisimal work done when extending a rod is given by SW = fdL. Which of the following Maxwell relations is derived from the internal energy? Select one: a. Ob. ² C. ○ d. Ꭲ (5) S - (355) f (F), = (²), T (²7) ₂ = ( 5 ) ₁ as S (2/²)₁ = − ( ³ ) ₁
Problem 2) Consider the following Maxwell Boltzmann distribution of molecular speeds: P(v) = 4( m 27kBT. mp² v²e 2kgT To calculate average values for say f(v) (function of v) one just integrates f(v) with P(v)dv from zero to infinity = P(v)f(v)dv, where signifies average of f(v). Of course, the distribution should be normalized: P(v)dv=1, (is a requirement for any probability distribution). a) Check the last equation. b) Calculate the average of v. c) Calculate the average of v². d) Calculate from c) the RMS value of the speed. e) Calculate the most probable value of v. f) Square the results of b, d and e and rank them from smallest to the largest value.