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Molecules of a Cal Poly Pomona ACME gas are crossing a given plane of a spherical shell unit area in unit time. Show that the average total kinetic energy of the molecules is K.E. = 2kT, where k = Boltzmann's constant. Recall, the emitted beam of molecules has a mean squared velocity jvaN JvdN and the volume of the shell is V = 47v°dv And thus, the fraction of molecules with velocities in the range v to v+dv is given by the Maxwell relation 3/2 m S(v)dv=|- exp(-mv² / 2kT47v*dv 2nkT Hint: Insert (3) into (1) and then formulate K.E. = 1/2m v² .

Molecules of a Cal Poly Pomona ACME gas are crossing a given plane of a spherical shell unit area in unit time. Show that the average total kinetic energy of the molecules is K.E. = 2kT, where k = Boltzmann's constant. Recall, the emitted beam of molecules has a mean squared velocity jvaN JvdN and the volume of the shell is V = 47v°dv And thus, the fraction of molecules with velocities in the range v to v+dv is given by the Maxwell relation 3/2 m S(v)dv=|- exp(-mv² / 2kT47v*dv 2nkT Hint: Insert (3) into (1) and then formulate K.E. = 1/2m v² .

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Molecules of a Cal Poly Pomona ACME gas are crossing a given plane of a spherical shell unit area in unit time. Show that the average total kinetic energy of the molecules is K.E. = 2kT, where k = Boltzmann's constant. Recall, the emitted beam of molecules has a mean squared velocity NPA| and the volume of the shell is V = 47v dv And thus, the fraction of molecules with velocities in the range v to v+dv is given by the Maxwell relation 3/2 m f(v)dv exp(-mv² / 2kT47v’dv 2nkT Hint: Insert (3) into (1) and then formulate K.E. = 1/2m v.
Transcribed Image Text:Molecules of a Cal Poly Pomona ACME gas are crossing a given plane of a spherical shell unit area in unit time. Show that the average total kinetic energy of the molecules is K.E. = 2kT, where k = Boltzmann's constant. Recall, the emitted beam of molecules has a mean squared velocity NPA| and the volume of the shell is V = 47v dv And thus, the fraction of molecules with velocities in the range v to v+dv is given by the Maxwell relation 3/2 m f(v)dv exp(-mv² / 2kT47v’dv 2nkT Hint: Insert (3) into (1) and then formulate K.E. = 1/2m v.
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