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Need clarity, kindly explain! The volume of air increases by 5% in its adiabatic expansion. The percentage decrease in its pressure will be

The volume of air increases by 5% in its adiabatic expansion. The percentage decrease in its pressure will be

  • Option 1)

    5%

  • Option 2)

    6%

  • Option 3)

    8%

  • Option 4)

    7%

 
Answers (1)
773 Views
V Vakul

As we learnt in

Equation of state -

dQ= 0

n\, C_{V}\, dT+PdV= 0
 

- wherein

On solving

\gamma \frac{dV}{V}+\frac{dP}{P}= 0

 

PV^{\gamma }= constant

On differentiating, we get

dP.V^{\gamma }+\gamma .V^{\gamma - 1}.PdV = 0

\Rightarrow dP = -\gamma \frac{P}{v}.dV

\frac{dP}{P} = -\gamma \frac{dV}{V} = -\left ( 1.4 \right )\times 5 \%=-7\%

 


Option 1)

5%

This option is incorrect

Option 2)

6%

This option is incorrect

Option 3)

8%

This option is incorrect

Option 4)

7%

This option is correct

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