Question

By how much should the pressure be increased in order to decrease the volume of a gas by 5% at a constant temperature?

• A. $5\%$
• B. $5.26\%$
• C. $10\%$
• D. $4.26\%$

Answer 1

The correct option is B $5.26\%$

Boyle's law states that at constant temperature, the product of pressure and volume is constant.

Assume the pressure and the volume of the gas at tnitial conditions to be $P_1,V_1$
and the pressure and the volume of the gas at final condition to be $P_2,V_2$

The final volume is decreased by 5% and therefore, $V_2=0.95V_1$

We can calculate $P_2$ from the equation,
$P_1{V}_1$ = $P_2{V}_2$

Hence $P_2=P_1(\frac{V_1}{0.95V_1}$)
= $P_2=1.0526P_1$

Now increase in pressure = $P_2-P_1$
= 0.526

In terms of percentage, the same can be expressed as 5.26%