Question

If a monoatomic gas is compressed adiabatically to \((1/27)^{\text{th\) of its initial volume, then its pressure becomes}

• A. \(27\) times
• B. \(125\) times
• C. \(243\) times
• D. \(81\) times
• E. \(64\) times

Hint:

For monoatomic gas in adiabatic change: \[ \gamma=\frac{5}{3} \] and powers simplify easily if volume ratio is a power of \(3\).

Answer 1

The Correct Option is C

For adiabatic process: \[ PV^\gamma=\text{constant} \] For monoatomic gas: \[ \gamma=\frac{5}{3} \] Given: \[ V_2=\frac{V_1}{27} \] So, \[ \frac{P_2}{P_1}=\left(\frac{V_1}{V_2}\right)^\gamma =27^{5/3} \] \[ 27^{5/3}=(3^3)^{5/3}=3^5=243 \] Hence, \[ \boxed{(C)\ 243\text{ times}} \]