Question

if the temperature is constant what change in volume would cause the pressure of an enclosed gas to increase by a factor of 4

Answer 1

Answer : The change in volume would be reduced to  $\frac{1}{4}$ of its original volume.

Explanation :

Boyle's Law : It is defined as the pressure of the gas is inversely proportional to the volume of the gas at constant temperature and number of moles.

$P\propto \frac{1}{V}$

or,

$P_1V_1=P_2V_2$

where,

$P_1$ = initial pressure

$P_2$ = final pressure = $4P_1$

$V_1$ = initial volume

$V_2$ = final volume

Now put all the given values in the above equation, we get:

$P_1\times V_1=4P_1\times V_2$

$\frac{V_2}{V_1}=\frac{1}{4}$

Thus, the change in volume would be reduced to  $\frac{1}{4}$ of its original volume.

Answer 2

P1V1=4P1V2
V2/V1= P1/4P1
V2/V1= 1/4
V2=1/4*V1
volume will decrease by factor 1/4