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  • In an adiabatic expansion of air the volume increases by The percentage change in pressure is <img alt="(\g

In an adiabatic expansion of air the volume increases by 100 \%. The percentage change in pressure is (\gamma=1.4)
 

Option: 1

14 \%


 


Option: 2

6 \% \mathrm{~W}
 


Option: 3

30 \%
 


Option: 4

140 \%


Answers (1)

best_answer

\mathrm{PV}^\gamma=\mathrm{k}\: \text{or} \: \mathrm{P}=\mathrm{kV}^{-\gamma}                    ..........(1)

Differentiating

\mathrm{\mathrm{dP}=\mathrm{k}(-\gamma) \mathrm{V}^{-\gamma-1} \mathrm{~d} \mathrm{~V}}                 ............(2)

Dividing equation (1) to (2) \mathrm{\frac{\mathrm{dP}}{\mathrm{p}}=\frac{-\gamma}{\gamma} \mathrm{dV}}

\mathrm{\frac{\mathrm{dP}}{\mathrm{p}} \times 100=\frac{-\gamma}{\gamma} \mathrm{dV} \times 100 \quad\quad{[\because \mathrm{dV}=\mathrm{V}] } }

\mathrm{ =1.4 \times 100=140 \% }



 

Posted by

Deependra Verma

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