Answered: Let's look at the term InN!. Compare… | bartleby

Related questions

Question

Let's look at the term InN!. Compare its exact value with the more
accurate one of Stirling's approximation,
EANt InN!=N/N-N+ [N
and to a lighter form.
(~N! ~ N/NN-N₁₂₁₂ (N=1₂10₂100)
Calculate the relative ellors of the approximations in all cases

Expert Solution

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

9.1. Consider the results for ideal gases derived from quantum mechanics. Write an expression for the function s(T, v) that includes the parameter A(T). (a) Show that the behavior of the entropy as T0 is unrealistic in a quantum sense. What approximation in the derivation is responsible for this behavior? (b) The Sackur-Tetrode equation is valid when the thermal de Broglie wave- length is much less than the average molecular separation distance, A(T) < (V/N)13, which is generally the case at high temperatures. Calculate the temperature at which this inequality is first violated for an ideal gas at atmospheric pressure and with a mass of 6.6 × 10-26 kg/molecule (which is typical of argon). x
The entropy S of a system of N spins, which may align either in the upward or in the downward direction, is given by S=-k,N|pln p+(1– p) In(1– p)] . Here k, is the Boltzmann constant. The probabinty of alignment in the upward direction is p. The value of p, at which the entropy is maximum, is (Give your answer upto one decimal place)
Problem 1: Consider a classical ideal gas in three dimensions, with N indistinguishable atoms confined in a box of volume N³. Assume the atoms have zero spin and neglect any internal degrees of freedom. Starting from the energy levels of a single atom in a box, find: (a) The Helmholtz free energy F' Hint: ſ. -ax² d.x e Va (b) The entropy o (c) The pressure p
Asystem consist of 5 indistinguishable particles, the total energy U=8£ , the degenerey gi = 4 for each energy level, the distribution of the particles on the energy levels shows in the figure (note that, there is no restriction on the number of particles on each energy state and there is no zeroth energy level). Calculate the entropy of the system( K3=8.62 x10 eVK'). k 1 2 3 4 5 6 N . EYE 4 3 2 . 1 :: .. w 5.59 x10-4 eVK-140 6.59 x10-5 eVK-1 80 7.59 x10-6 eVK-1.00
calculate the heat capacity of an Einstein solid in the low-temperature limit. Sketch the predicted heat capacity as a function of temperature. (Note: Measurements of heat capacities of actual solids at low temperatures do not confirm the prediction that you will make in this problem.
Number 3 please
Consider a classical ideal gas of N diatomic heterogeneous molecules at temperature T. The charac- teristic rotational energy parameter is € = 1 and the natural frequency of vibrations is wo. Consider the temperature region where T≫er/kB, but T is of the order of ħwo/kB. Ignore contributions from all other internal modes. Calculate the canonical partition function, the average energy, and the heat capacity at constant volume, Cv.
Calculate the partition function of a two-level system at 25 °C with an energy gap of 10-2¹ J, assuming: a) Both states are non-degenerate. b) The ground state is non-degenerate, and the excited state is 3-fold degenerate.