An ideal gs at pressure P is adiabatically compressed so that its density becomes n times the initial vlaue The final pressure of the gas will be `(gamma=(C_(P))/(C_(V)))`

Options

A. `ngammaP`
B. `(n-gamma)P`
C. `n(gamma-1)P`
D. `n(1-gamma)P`

Answer

A

Explanation

For an adiabatic process , `PV^(gamma)` =constant
`P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
where subscripts 1 and 2 represent the initial and final states respectively
or `(P_(2))/(P_(1))=(V_(1))/(V_(2))^(gamma)=(P_(2))/(P_(1))^(gamma)=(nP_(1))/(P_(1))^(gamma)`
or `P_(2)=P_(1)n^(gamma)=n^(gamma)P`