Heat and Thermodynamics 4 Question 41

44. A cubical box of side 1m contains helium gas (atomic weight 4 ) at a pressure of 100N/m2. During an observation time of 1s, 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=253J/molK and k=1.38×1023J/K.

(2002,5M)

(a) Evaluate the temperature of the gas.

(b) Evaluate the average kinetic energy per atom.

(c) Evaluate the total mass of helium gas in the box.

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Solution:

  1. Volume of the box =1m3

Pressure of the gas =100N/m2

Let T be the temperature of the gas. Then,

(a) Time between two consecutive collisions with one wall =1500s. This time should be equal to 2lvrms, where l is the side of the cube.

2lvrms=1500 or vrms=1000m/s( as l=1m) or 3RTM=1000T=(1000)2M3R=(10)6(4×103)3(25/3)=160K

(b) Average kinetic energy per atom

=32kT=32(1.38×1023)(160)J=3.312×1021J

(c) From pV=nRT=mMRT

We get mass of helium gas in the box, m=pVMRT

Substituting the values, we get

m=(100)(1)(4)(25/3)(160)=0.3g



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