Question

An ideal gas at pressure P is adiabatically compressed so that its density becomes n times the initial value. The final pressure of the gas will be

• A. n$\gamma$P
• B. (n – $\gamma$)P
• C. n( $\gamma$ – 1)P
• D. n(1 – $\gamma$)P

Answer 1

Answer: (A)

n$\gamma$P

Answer 2

: for an adiabatic process,

$\mathrm { PV } ^ { \gamma }$ = constant

$\therefore P _ { 1 } V _ { 1 } ^ { \gamma } = P _ { 2 } V _ { 2 } ^ { \gamma }$

Where subscripts 1 and 2 represent the initial and final states respectively.

Or $\frac { P _ { 2 } } { P _ { 1 } } = \left( \frac { V _ { 1 } } { V _ { 2 } } \right) ^ { \gamma } = \left( \frac { \rho _ { 2 } } { \rho _ { 1 } } \right) ^ { \gamma } = \left( \frac { n \rho _ { 1 } } { \rho _ { 1 } } \right) ^ { \gamma }$

Or $P _ { 2 } = P _ { 1 } n ^ { \gamma } = n ^ { \gamma } P \quad \left( \because P _ { 1 } = P \right)$