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CBSE Class 11-science Answered

an ideal gas is enclosed in a cylinder at pressure 2 atm and temperature 300k the mean time between two successive collisions is 6×10–⁸s if the pressure is doubled and temperature is increased to 500k the mean time between two successive collisions will be close to
Asked by ifrayaseen31 | 28 Oct, 2023, 09:26: AM
answered-by-expert Expert Answer
Initial pressure P = 2 atm ; Final pressure = 5 atm ;
 
Initial temperature = 300 K ; final temperature = 500 K
 
 
Mean free path λ between moleculer collisions is ,   begin mathsize 14px style lambda space equals space fraction numerator k space T over denominator square root of 2 space straight pi space straight d squared space space straight P end fraction end style
 
where k is Boltzman constant , T is temperature , d is moleculer size and P is pressure .
 
Mean free path λ between moleculer collision is directly proportional to temperature T and
inversely proportional to pressure P
 
Average speed vavg  of gas molecules  is proportional to square root of temperature ,
 
begin mathsize 14px style v subscript a v g end subscript space proportional to space square root of T end style
 
Mean time τ between collision = ( mean free path ) / ( average speed )
 
( please note that τ in above expression is greek symbol tau not temperature )
 
begin mathsize 14px style tau space space proportional to space fraction numerator T over denominator P space square root of T end fraction end style
 
 
begin mathsize 14px style tau space space proportional to space fraction numerator square root of T over denominator P space end fraction end style
 
Hence mean time between collision at 500 K and 4 atm. pressure is calculated as 
 
begin mathsize 14px style tau space equals space 6 space cross times space 10 to the power of negative 8 end exponent space cross times space square root of 500 over 300 end root cross times 2 over 4 space space equals space 3.873 space cross times space 10 to the power of negative 8 end exponent space s end style
 
 
 
 
Answered by Thiyagarajan K | 28 Oct, 2023, 11:24: AM

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CBSE 11-science - Physics
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