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
$PV=P_{1} \, V_{1}= \, P_{2} \, V_{2}$
$PV= \, \frac{99}{100}PV_{2}$
$V_{2}= \, \frac{100}{99} \, V$