Question

The pressure and volume of a gas are P and V respectively. It is compressed suddenly to $1/32$ of its initial volume then its final pressure will be:

• A. $32P$
• B. $128P$
• C. $P/128$
• D. $P/32$

Answer 1

The correct option is B $128P$

Given: Initial volume of gas = V

Initial pressure of gas = P

Solution: As we know,

$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$ (1)

For diatomic gases,

$\gamma =1.4$

Also, $V_2=\frac{V_1}{32}$ (given)

So, from equation (1) the final pressure of gas is given by,

$P_2=P_1\times (\frac{V_1}{V_2}{)}^{\gamma }$

On subtituting the values we get,

$P_2=P_1\times {\left(\frac{V_1}{\frac{V_1}{32}}\right)}^{1.4}$

Therefore, $P_2=128P_1$

Hence, the correct option is (B).