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Equations 20.43 and 20.44 show that for a collection of gas particles, which turns out to be true whenever the particles have a distribution of speeds. Let us explore this inequality for a two-particles gas. Let the speed of one particle be and the other particle has a speed . 

(a) Show that the average of these two speeds is .

(b) Show that .  

(c) Argue that the equation in part (b) proves that, in general, .

(d) Under what special condition will for the two-particle gas?

 

  

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Aerielle Anne Beltran
Aerielle Anne BeltranLv10
21 Nov 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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Review. Rail guns have been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Fig. P29.42) consists of two long, parallel, horizontal rails l=3.50 cm apart, bridged by a bar of mass m=3.00 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I=24.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure P29.42 shows the bar at rest at the midpoint of the rails at the moment the current is established. We wish to find the speed with which the bar leaves the rails after being released from the midpoint of the rails.

(a) Find the magnitude of the magnetic field at a distance of 1.75 cm from a single long wire carrying a current of 2.40 A.

(b) For purposes of evaluating the magnetic field, model the rails as infinitely long. Using the result of part (a), find the magnitude and direction of the magnetic field at the midpoint of the bar.

(c) Argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. At other points along the bar, the field is in the same direction as at the midpoint but is larger in magnitude. Assume the average effective magnetic field along the bar is five times larger than the field at the midpoint.

With this assumption, find (d) the magnitude and (e) the direction of the force on the bar.

(f) Is the bar properly modeled as a particle under constant acceleration?

(g) Find the velocity of the bar after it has traveled a distance d=130 cm to the end of the rails.

Review. Rail guns have been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Fig. P29.42) consists of two long, parallel, horizontal rails l= 3.50 cm apart, bridged by a bar of mass m = 3.00 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I = 24.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure P29.42 shows the bar at rest at the midpoint of the rails at the moment the current is established. We wish to find the speed with which the bar leaves the rails after being released from the midpoint of the rails. (a) Find the magnitude of the magnetic field at a distance of 1.75 cm from a single long wire carrying a current of 2.40 A. (b) For purposes of evaluating the magnetic field, model the rails as infinitely long. Using the result of part (a), find the magnitude and direction of the magnetic field at the midpoint of the bar (c) Argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. At other points along the bar, the field is in the same direction as at the midpoint, but is larger in magnitude. Assume the average effective magnetic field along the bar is five times larger than the field at the midpoint. With this assumption, find (d) the magnitude and (e) the direction of the force on the bar. (f) Is the bar properly modeled as a particle under constant acceleration? (g) Find the velocity of the bar after it has traveled a distance d = 130 cm to the end of the rails.

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