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Adiabatic compressibility of an ideal gas at a pressure \mathrm{P} is
 

Option: 1

\mathrm{\gamma \mathrm{P}}
 


Option: 2

\mathrm{\frac{\gamma}{\mathrm{P}}}

 


Option: 3

\mathrm{\frac{1}{\gamma \mathrm{P}}}
 


Option: 4

None of these


Answers (1)

In adiabatic process \mathrm{\mathrm{PV} \gamma= constant }           \mathrm{\quad \Rightarrow \quad \mathrm{P}^\gamma \mathrm{V}^{\gamma-1}+\mathrm{V}^\gamma}\mathrm{\frac{d P}{d V}=0 }

\mathrm{\Rightarrow \frac{d P}{d V}=-\frac{\gamma P}{V}}

Bulk modulus \mathrm{\mathrm{B}=-\mathrm{V} \frac{\mathrm{dP}}{\mathrm{dV}}}

                         \mathrm{=\gamma \mathrm{P} }

compressibility \mathrm{\mathrm{C}=\frac{1}{\mathrm{~B}}=\frac{1}{\gamma \mathrm{P}} }





 

Posted by

Kshitij

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