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Q.

A cubical box of side 1 m contains helium gas (atomic weight 4) at a pressure of   100 Nm–2. During an observation time of 1 second, an atom travelling with root- mean-square speed parallel to one of the edges of the cube was found to make  500 hits with a particular wall, without any collision with other atoms. Take R =  253  J mol–1K–1  and k = 1.38×10–23J K–1. Evaluate average kinetic energy.

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a

3.312×10–21J

b

6.412×10–21J

c

6.412×10–20J

d

8.143×10–20J

answer is A.

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Detailed Solution

Distance travelled in one second  =500×2m=1000m.  So, vRMS=1000 ms−1But  vRMS=3RTM⇒T=160KAverage kinetic energy per atom =  32kT=32×1.38×10–23×160 = 3.312×10–21J
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A cubical box of side 1 m contains helium gas (atomic weight 4) at a pressure of   100 Nm–2. During an observation time of 1 second, an atom travelling with root- mean-square speed parallel to one of the edges of the cube was found to make  500 hits with a particular wall, without any collision with other atoms. Take R =  253  J mol–1K–1  and k = 1.38×10–23J K–1. Evaluate average kinetic energy.