A 10-cm cubical box is filled with gas. Suppose a particular atom starts at the

Question

A 10-cm cubical box is filled with gas. Suppose a particular atom starts at the center as shown. It is observed that when the temperature is 300 K the average time < t > before the atom strikes a wall is 50 sec.

If the temperature is increased to 330 K, what is the new value of < t >?

(a) < t > = 45.5 sec
(b) < t > = 52.5 sec
(c) < t > = 47.7 sec
(d) < t > = 55.0 sec
(e) < t > = 60.5 sec




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QUESTION 13**
Suppose that we repeat the measurement in a box of 20 cm on a side, with the gas pressure and temperature not changed (i.e., T remains at 300 K). What is the value of < t > in this case?
(a) < t > = 35 sec
(b) < t > = 100 sec
(c) < t > = 200 sec
(d) < t > = 71 sec
(e) < t > = 400 sec

Explanation / Answer

kinetic energy = KT= 1/2 mv2 = C * (distance/time)2 where C and K are constants

in problem 1

T1/T2 = (t2/t1)2

so t2 = 47.67

in problem 2

d1/d2 = t1/t2

t2 = 20/10 * 50 = 100sec

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