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Question

A cubical box is side 1 meter contains helium gas(atomic weight 4) at a pressure of 100N/m2. During an observation time of 1 second, an atom travelling with the 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-K and k=1.38×1023 J/K.
Evaluate the temperature of the gas.

A
T=360K.
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B
T=160K.
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C
T=260K.
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D
T=460K.
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Solution

The correct option is B T=160K.
The volume of the box 1m3
Pressure of the gas =100N/m2
Time between two consecutive collisions with one wall =1500s

Let T be the temperature of the gas
The time of collision should be equal to 2lvrms, where l is the length of the cube.

So, 2lvrms=1500

vrms=1000m/s

The RMS velocity of the particle is given by:
vrms=2RTM

2RTM=1000

T=(1000)2M3R=(106)(4×103)3(253)=160K

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