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
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.