Question

The pressure P1 and density d1 of a diatomic gas ($\gamma$ = 7/5) change to P2 and d2 during an adiabatic operation. If $\frac { \mathrm { d } _ { 2 } } { \mathrm {~d} _ { 1 } }$ = 32, then is

• A. 76
• B. 128
• C. 168
• D. 298

Answer 1

Answer: (B)

128

Answer 2

: in an adiabatic operation

$\therefore \frac { P _ { 2 } } { P _ { 1 } } = \left( \frac { V _ { 1 } } { V _ { 2 } } \right) ^ { \gamma } = \left( \frac { m } { d _ { 1 } } \times \frac { d _ { 2 } } { m } \right) ^ { \gamma } = \left( \frac { d _ { 2 } } { d _ { 1 } } \right) ^ { \gamma }$

$\therefore \frac { P _ { 2 } } { P _ { 1 } } = ( 32 ) ^ { 7 / 5 } = \left( 2 ^ { 5 } \right) ^ { 7 / 5 } = 2 ^ { 7 } = 128$

$\therefore \frac { P _ { 2 } } { P _ { 1 } } = 128$