Question

By what percentage should the pressure of a given mass of gas be increased so as to decrease its volume by 10$\%$ at a constant temperature?

• A. $8.1\%$
• B. $9.1\%$
• C. $10.1\%$
• D. $11.1\%$

Answer 1

The correct option is D $11.1\%$

At a constant temperature
$T_i=T_f=T$
Let
Initial pressure $\left(P_i\right)=P$
Final pressure $\left(P_f\right)=P^{\prime }$
Initial volume $\left(V_i\right)=V$
Final volume$\left(V_f\right)=0.9V$
From ideal gas equation, at a constant temperature, we can write that,
$PV=$ constant
$\Rightarrow P_i{V}_i=P_f{V}_f$
$\Rightarrow PV=P^{\prime }\times \frac{90}{100}V$
$\Rightarrow \frac{P^{\prime }}{P}=\frac{100}{90}=1+\frac{10}{90}$
$\Rightarrow \frac{P^{\prime }}{P}-1=\frac{P^{\prime }-P}{P}=\frac{10}{90}$
$\therefore \text{\% increase in pressure}=\frac{10}{90}\times 100=11.1\%$
Hence, the correct answer is option (d).