Calculate the ratio of new volume to old volume

[Richie Smash]

Homework Statement

A car tyre has initial temperature 23°C and inital pressure 2*10⁵ Pa
After heating in the sun, temperature is now 34°C and final pressure is 2.1*10⁵Pa

Question asks, Calculate the ratio of new volume to old volume (V₁/V₂) if the pressure is held constant during the temperature rise stated above.

Homework Equations

General Gas Equation

(P1V1)/T1= (P2V2)/T2

The Attempt at a Solution

Using the general gas Equation I worked out the final pressure of 2.1*10⁵Pa which was not orignially given.

Now for the ratio my idea is as follows

If the pressure is held constant, then V1/T1= V2/T2 which is a statement of charles Law.

I'm not sure how to find the ratio but perhaps if the ratio of new to old volume would be the same as the ratio between new and old temperature?

SO I would convert the celciusto kelvin by adding 273 and obtain 296 Kelvin initial temperature, and 307 K final temperature

Then I would do this 307/296 and that would give me 1.04 to two significant figures as the ratio.

Is this correct? I would like some assistance.

 

[haruspex]

perhaps if the ratio of new to old volume would be the same as the ratio between new and old temperature?

That is what Charles' Law says. Just rearrange the equation to that form.

Is this correct?

Yes.

 

[Richie Smash]

Oh ok thanks a lot! I shall re arrange the equation for further clarification