Question

A gas at NTP is suddenly compressed to one-fourth of its original volume. If $\gamma$ is supposed to be $\frac { 3 } { 2 }$ , then the final pressure is

• A. 4 atmosphere
• B. $\frac { 3 } { 2 }$ atmosphere
• C. 8 atmosphere
• D. $\frac { 1 } { 4 }$ atmosphere

Answer 1

Answer: (C)

8 atmosphere

Answer 2

$P V ^ { \gamma } =$ constant $\Rightarrow \frac { P _ { 2 } } { P _ { 1 } } = \left( \frac { V _ { 1 } } { V _ { 2 } } \right) ^ { \gamma }$ $\Rightarrow \frac { P _ { 2 } } { 1 } = \left( \frac { V _ { 1 } } { V _ { 1 } / 4 } \right) ^ { 3 / 2 } = 8$

⇒ $P _ { 2 } = 8 \mathrm {~atm}$.