Question

For $5$% increase in volume and temperature, what will be the net effect on pressure for $2$ moles of a gas enclosed in a chamber?

• A. Remain same
• B. Decreased by $10$%
• C. Increased by $5$%
• D. Increased by $10.5$%

Answer 1

The correct option is A Remain same

Volume is increased by $5$%.
So assuming initial volume $V$.
$V_2=(V+\frac{5\times V}{100})=1.05V$

Temperature is increased by $5$%.
So assuming initial temperature $T$.
$T_2=(T+\frac{5T}{100})=1.05T$

Now, $PV=nRT$
$\Rightarrow P_2=\left(\frac{nR{T}_2}{V_2}\right)$
$P_2=\frac{nR\times 1.05\times T}{1.05V}$
$P_2=\frac{nRT}{V}.....\left(i\right)$
We have initially $PV=nRT$
$\Rightarrow P=\frac{nRT}{V}.....\left(ii\right)$

By comparing the two equations we can conclude that $P$ remain unchanged.

Why this question? This question helps you in concept related to percentage change and their impact on other quantities.