To show that: (a) if the expressions for Maxwell’s speed distribution energies for molecules in a gas is as given in Chapter 19, then the most probable energy is given by K p = ½ kT Also verify the result with the energy distribution curve given in Fig 43.10 in the textbook, for T = 1.5x10 7 K. (b) the most probable speed is given by v p = 2 k T m , then find its value for protons at T = 1.5x10 7 K. (c) the energy corresponding to the most probable speed (which is not the same as most probable energy) is K v, p = kT And locate this quantity of the curve given in Fig 43.10.

Question

Want to see the full answer?

Answer 1

Question

Chapter 43, Problem 56P

To determine

To show that:

(a) if the expressions for Maxwell’s speed distribution energies for molecules in a gas is as given in Chapter 19, then the most probable energy is given by

K_p = ½ kT

Also verify the result with the energy distribution curve given in Fig 43.10 in the textbook, for T = 1.5x10⁷K.

(b) the most probable speed is given by

vp= 2kTm,

then find its value for protons at T = 1.5x10⁷K.

(c) the energy corresponding to the most probable speed (which is not the same as most probable energy) is

K_{v, p} = kT

And locate this quantity of the curve given in Fig 43.10.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Assume a hydrogen atom is a sphere with diameter 0.100 nm and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at 08C and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 fm

The degeneracy pressure of the electrons can stabilize the collapse of a star due to gravity by equating the gravitational inward pressure with the outward electron gas degeneracy pressure. These cold stars called white dwarfs have small radii compared to their original size and this radius decreases as the original mass of the star increases. As the mass of a star increases, the electron energy increases to a point in which their energy has to be treated relativistically. (a) Evaluate the degeneracy pressure for ultra-relativistic electrons (problem 2, above). (b) As the pressure increases, the reaction e − + p → n + ν takes place. The neutrinos (ν) escape as matter is transparent to them, electrons and protons convert to neutrons until we are left with a neutron star. Using your expression for the degeneracy pressure obtained in (a) above, equate the gravitational pressureto the neutron degeneracy pressure (replace the electron’s mass in your degeneracy pressure expression from (a)…

You are performing work as an assistant to a cosmology professor. She asks you to estimate the temperature of the Universe at a time after the Big Bang when neutral atoms could form from the plasma and the Universe became transparent. She tells you that the energy required to excite an atom is on the order of 1 eV. She suggests you use the Boltzmann distribution function e-E/k BT to find the order of magnitude of the threshold temperature at which 1.00% of a population of photons has energy greater than 1.00 eV.