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- The population ratio between two energy levels ni nj separated in energy by: A E = E₁ - Ej with AE = 1.1×10-22 J is 0.84. That is: ni = 0.84 with AE = 1.1×10-22] nj Remember the Boltzmann equation for the population of particles in state i with energy Ei at temperature T is: N n₁ = = e Z What is the temperature of the system (use two sig figs)? 4.0 ✓ Karrow_forwardHow to solve this questionarrow_forward3. The classical partition function of a gas of noninteracting indistinguishable particles is written as exp{- N! 2m Z= where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x³xdx = Va Hint:arrow_forward
- A valid, but probably useless, dimensionless group is givenby (μT0g)/ (YLα) , where everything has its usual meaning,except α . What are the dimensions of α ?( a ) θL-1T-1 , ( b ) θL-1T-2 , ( c ) θML-1 , ( d ) θ-1LT-1 ,( e ) θLT-1arrow_forwardOne-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 + eBhwarrow_forwardFigure 1 of 1 > Energy (J) 4. 3. 2- 1- 1,2-1 +. -1 -21 K, + U, +Wt= K, + U, + AE %3D ext |||arrow_forward
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