Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
Question
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Chapter 13, Problem 85P

(a)

To determine

The average distance between Ping-Pong balls at any instant.

(a)

Expert Solution
Check Mark

Answer to Problem 85P

Average distance of separation is 52cm.

Explanation of Solution

Diameter of ball is 3.75cm and diameter of N2 molecule is 0.30nm.

It is assumed that the N2 molecules are located at the centre of a sphere.

Write the equation to find the average distance of separation between Ping-Pong balls at any instant.

dav=adn2 (I)

Here, dav is the average distance between Ping –Pong balls (same as diameter of spheres), a is the scale factor, and dn2 is the separation between N2 molecules.

Write the equation for a.

a=dpingdn2 (I)

Here, dping is the diameter of Ping-Pong balls.

Write the equation for each ping pong ball.

VN=16πdav3

Here, V is the total volume occupied by spheres and N is the Avogadro number.

Rewrite the above relation in terms of dav.

dav=(6VπN)1/3 (II)

Rewrite equation (I) by substituting equations (II) and (III).

dav=(dpingdn2)(6VπN)1/3

Conclusion:

Substitute 3.75cm for dping, 0.30nm for dn2, 0.0224m3 for V, and 6.022×1023 for N in the above equation to find dav.

dav=(3.75cm(102m1cm)0.30nm(109m1nm))(6(0.0224m3)π(6.022×1023))1/3=(12.5×107)(0.0416×107m)=0.52m(102cm1m)=52cm

Therefore, the average distance of separation is 52cm.

(b)

To determine

The average distance travelled by Ping-Pong balls before collision with one another.

(b)

Expert Solution
Check Mark

Answer to Problem 85P

Average distance travelled is 12m.

Explanation of Solution

Diameter of ball is 3.75cm and diameter of N2 molecule is 0.30nm.

It is assumed that the N2 molecules are located at the centre of a sphere.

Write the equation for mean free path.

Λ=12πdn22(N/V)

Here,Λ is the mean free path.

Write the relation between N/V and pressure.

NV=PKBT

Here, KB is the Boltzmann constant, T is the temperature, and P is the pressure.

Rewrite the equation for Λ by substituting the above relation.

Λ=12πdn22(PKBT)=KBT2πdn22P

Write the average distance travelled by Ping-Pong balls before collision with one another.

dcol=aΛ

Here, dcol is the average distance travelled by Ping-Pong balls before collision with one another.

Rewrite the above relation by substituting P2πdn22KBT for Λ.

dcol=aKBT2πdn22P

Rewrite the above relation by substituting equation (I).

dcol=(dpingdn2)KBT2πdn22P

Conclusion:

Substitute 3.75cm for dping, 0.30nm for dn2, 1.38×1023J/K for KB, 273.15K+0.0K for T, 3.14 for π, 0.30nm for dn2, and 1.00atm for P in the above equation to find dcol.

dcol=(3.75cm(102m1cm)0.30nm(109m1nm))(1.38×1023J/K)(273.15K+0.0K)2(3.14)(0.30nm(109m1nm))(1.00atm(1.013×105Pa/atm1.00atm))=14.13×1023Jm1.18×11023J=12m

Therefore, the average distance travelled is 12m.

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Chapter 13 Solutions

Physics

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