pls help me to solve the 59th question

Asked by thejasvi001 | 2nd Jan, 2021, 07:49: PM

Expert Answer:

Fast and sudden expansion of gas is adiabatic process.
 
For adiabatic expansion of gas, we have,  
 
begin mathsize 14px style p subscript i v subscript i superscript gamma space equals space p subscript f v subscript f superscript gamma end style  ......................(1)
where p is pressure and v is volume . subscript i stands for initial state and subscript f stands for final state.
γ is ratio of specific heat .
 
we are given that , specific heat at constant volume , Cv = 2R
 
we have , Cp - Cv = R  , where Cp is specific heat at constant pressure.
 
Hence Cp = 2R+R = 3R  and γ = ( Cp / Cv ) = (3R / 2R ) = 1.5 
 
Hence ratio of initial pressure to final pressure is determined from eqn.(1) as
 
begin mathsize 14px style p subscript i over p subscript f equals open parentheses v subscript f over v subscript i close parentheses to the power of gamma space equals space 3 to the power of 1.5 end exponent space almost equal to space 5.2 end style
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Answer :- Ratio of initial to final pressure is nearly equal to 5

Answered by Thiyagarajan K | 2nd Jan, 2021, 09:25: PM

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