Question

The pressure and volume of a given mass of gas at a given temperature are $P$ and $V$ respectively. Keeping the temperature constant, the pressure is increased by $10\%$ and the system is allowed to achieve a steady-state, then the pressure is decreased by $10\%$ . What can be said about the final volume?

• A. less than $V$
• B. more than $V$
• C. equal to $V$
• D. less than $V$ for diatomic and more than $V$ for monoatomic

Answer 1

Answer: (B)

When pressure is increased by 10%
$P_1=P\left(1+\frac{10}{100}\right)=\frac{11}{10}P$
Then presser is decreased by 10%
$P_2=P_1\left(1-\frac{10}{100}\right)=\frac{9}{10}{P}_1$
$P_2=\frac{9}{10}\left(\frac{11}{10}P\right)=\frac{99}{100}P$
Then temperature is constant
$PV=P_1{V}_1=P_2{V}_2$
$PV=\frac{99}{100}P{V}_2$
$V_2=\frac{100}{99}V$