Question

At constant temperature on increasing the pressure of a gas by 5% will decrease its volume by

• A. 5%
• B. 5.26%
• C. 4.26%
• D. 4.76%

Answer 1

The correct option is D 4.76%

If $P_1=P$ then $P_2=P+$ 5% of P = 1.05 P
From Boyle's law PV=constant $\therefore \frac{V_2}{V_1}=\frac{P_1}{P_2}=\frac{P}{1.05P}=\frac{100}{105}$

Fractional change in volume$=\frac{\Delta V}{V}=\frac{V_2-V_1}{V_1}=\frac{100-105}{105}=-\frac{5}{105}$
$\therefore$ Percentage change in volume $\frac{\Delta V}{V}\times 100\%=-\frac{5}{105}\times \%=-4.76\%$ i.e. volume decrease by $4.76$