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

Taking into account the Boyle's law, the change in volume would be reduced by a factor of 4 of its original volume.

Boyle's law

The gas laws are a set of chemical and physical laws that allow us to determine the behavior of gases in a closed system. The parameters evaluated in these laws are pressure, volume, temperature, and moles.

Boyle's law is a gas law that relates pressure and volume. This law says that the volume occupied by a given mass of gas at constant temperature is inversely proportional to the pressure.

Boyle's law is expressed mathematically as:

Pressure×Volume=constant

or P×V=k

Now it is possible to assume that you have a certain volume of gas V₁ which is at a pressure P₁ at the beginning of the experiment. If you vary the volume of gas to a new value V₂, then the pressure will change to P₂, and the following will be true:

P₁×V₁=P₂×V₂

This case

In this case, you know:

• P₁= initial pressure
• V₁= initial volume
• P₂= final pressure= 4×P₁
• V₂= final volume

Replacing in Boyle's law:

P₁×V₁=4×P₁×V₂

Solving:

$V_{2} =\frac{P_{1} x V_{1} }{4xP_{1} }$

$V_{2} =\frac{V_{1} }{4 }$

Finally, the change in volume would be reduced by a factor of 4 of its original volume.

Learn more about Boyle's law:

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