In an adiabatic process on a gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about

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KollegeApply · Accepted Answer

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 = $\frac{7}{5}$ => "V'"^gamma/("V'"^gamma) = "P"/"P'" => ("V'"/"V")^ gamma = P/("P"+(0.5"p")/100) => ("V'"/"V")^($\frac{7}{5}$) = $\frac{100}{100}$.5 => "V'"/"V" = ($\frac{100}{100}$.5)^($\frac{5}{7}$) = ($\frac{200}{201}$)^($\frac{5}{7}$) => "V'"/"V" = 0.99644` $\Rightarrow$ V' = 0.99644 V $\Rightarrow$ V' =V -0.00356 V Therefore, V' is 0.36 % less than V.

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