# The volume of a gas decreases to half of its original volume, but the gas maintains the same number

###### Question:

## Answers

It will double.

Explanation:

For a gas at constant temperature and constant number of moles, we can use Boyle's law, which states that the product between pressure and volume of the gas is constant:

[tex]PV=const.[/tex]

This relationship implies that the pressure and the volume are inversely proportional. The previous equation can also be rewritten as

[tex]P_1 V_1 = P_2 V_2[/tex]

where P1 is the initial pressure of the gas, V1 the initial volume, P2 the final pressure and V2 the final volume. The problem says that the volume of the gas decreases to half of its original volume, so we can write

[tex]V_2 = \frac{V_1}{2}[/tex]

Substituting into the previous equation, we can find the new pressure of the gas:

[tex]P_2 = \frac{P_1 V_1}{V_2}=\frac{P1 V_1}{V_1 /2 }=2 P_1[/tex]

Therefore, the final pressure is twice the initial pressure.

By Boyles Law for an Ideal Gas, if the temperature is constant:

P1 V1 = P2 V2 where P and V are the pressures and volumes.

So here we have the volume change V1 >0.5 V1:-

P1 V1 = P2 * 0.5V1

P2 /P1 = V1 / 0.5V1 = 2

So the pressure will double.

It's choice A.

Pressure will be doubled if volume of gas decreases to half of its original volume

Explanation:

Ideal gas law:

where, P is pressure, V is volume, n is number of moles, R is gas constant and T is temperature in kelvin scale.

Here n and T are constants. Also R is a constant,

Hence we can write,

where, and are initial and final pressure respectively. and are initial and final volume respectively.

Here,

So,

or,

So, pressure will be doubled if volume of gas decreases to half of its original volume

The correct answer is option A.

Explanation:

Let the initial volume of the gas be [tex]V_1[/tex]

Initial pressure of the gas [tex]P_1[/tex]

When the volume of the gas decreases to half of the initial value.

Final volume of the gas = [tex]V_2=\frac{1}{2}V_1[/tex]

Final pressure of the gas = [tex]P_2[/tex]

According to Boyle's law:

[tex]P_1\times V_1=P_2\times V_2[/tex]

[tex]P_2=\frac{V_1\times P_1}{V_2}=\frac{V_1\times P_1}{\frac{1}{2}V_1}[/tex]

[tex]P_2=2\times P_1[/tex]

Hence, the correct answer is option A.

According to the ideal gas law, the pressure of the gas will most likely double. The correct option among all the options that are given in the question is the first option. The other choices given can be easily negated. I hope that this is the answer that has actually come to your great help.

The pressure will double because

Let

initial pressure be P1 and

final pressure be P2.

Initial volume will be V then,

final volume will be V/2 (as per question).

Now we have,

P1V1 = P2V2

So, according to our question

P1V = P2V/2

P1 x V /(V/2) = P2

P2 = 2P1.

Therefore, final pressure will be double of initial pressure.

Thanks.