# What happens to the volume if the temperature decreases from 300K to 200K? Consider the following changes imposed upon a sample of gas, assuming the variables remain constant Please explain...

What happens to the volume if the temperature decreases from 300K to 200K?

*Consider the following changes imposed upon a sample of gas, assuming the variables remain constant*

*Please explain further.*

*(use combined gas law)*

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### 2 Answers

The combined gas law is:

P1V1/T1 = P2V2/T2

Where P1 & P2 are the initial and final pressures; V1 & V2 are the initial and final volumes; and T1 and T2 are the initial and final temperatures in degrees K.

In this problem it is assumed that the pressure remains constant so P1 = P2

Substitute in what you know:

P1V1/300 = P1V2/200

divide by P1 and you get:

V1/300 = V2/200

rearrange and solve for V2:

V2 = 2/3 V1

In other words, the final volume will be 2/3 the initial volume.

`(P1xxV1)/(T1) = (P2xxV2)/(T2)`

This is the combined gas law.

We know that the temperature has been decreased.

If the pressure is held constant...

We only need to focus on this part of the equation:

V1 / T1 = V2 / T2

If the temperature goes down, to maintain the equality, then the volume must go down as well.

The same would be true for pressure if volume was held constant.

This also makes sense considering what we know about the kinetic theory of gases. Decreasing temperature decreases the average kinetic speed which decreases the the amount of force in which the particles collide against the side of their container. This could lower either the pressure exerted, or the volume of space taken up by the particles depending on what is held constant.