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Question
In an adiabatic process on a gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about
Options
0.36%
0.5%
0.7%
1%
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Solution
0.36 %
Let p and p, be the initial and final pressures of the system and V and V, be the initial and final volumes of the system. p, is 0.5% more than p and the process is adiabatic. So,
`"p"^("V"gamma) = "p'"^("V'"gamma) , gamma = 1.4 = 7/5`
`=> "V'"^gamma/("V'"^gamma) = "P"/"P'"`
`=> ("V'"/"V")^ gamma = P/("P"+(0.5"p")/100)`
`=> ("V'"/"V")^(7/5) = 100/100.5`
`=> "V'"/"V" = (100/100.5)^(5/7) = (200/201)^(5/7)`
`=> "V'"/"V" = 0.99644`
⇒ V' = 0.99644 V
⇒ V' =V -0.00356 V
Therefore, V' is 0.36 % less than V.
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