Ideal Gas and finding final pressure

[puniverse]

Homework Statement

I'm trying to understand algebraically how the solution was arrived at for the following problem.

Automobile tire at normal atmosphere at 10 deg C.
Inflating the tire to 28% of original volume with an increase in temp to 40 deg C
What is the pressure?

Homework Equations

PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is a constant, and T is the temp

The Attempt at a Solution

The the solution is given in what appears as a ratio between the initial values and final values, and I'm just not understanding algebraically how the equation in step 1. was derived. Why would I divide the final values with the initial values?

1. (P_2)(V_2) / (P_1)(V_1) = nRT_2 / nRT_1

2. (P_2)(.28V_1) / (1 atm)(V_1) = T_2 / T_1

3. (.28)P_2) / (1 atm) = 313.15 K / 283.15 K

4. P_2 = 1.106 / .28

5. P_2 = 3.95 atm


Thanks for whatever enlightenment you might be able to give.

 

[Jazz House]

Looks to me as if you need to use the Combined gas equation.

 

[Delzac]

Welcome to PF puniverse!

In this case, you can take it as this R = PV/nT, and since R is a constant regardless or what happens, they equate both sides together and shifted the variables around.

 

[puniverse]

Oh, I understand that. So it's like:

1. nR_1 = (P_1)(V_1) / T_1

2. nR_2 = (P_2)(V_2) / T_2

3. nR_1 = nR_2

4. (P_1)(V_1) / T_1 = (P_2)(V_2) / T_2 ... and then solve for P_2

Yup, that works. Thanks!

Quick question tho, would I be misunderstanding if I considered n a constant also? I mean, n as in the number of moles doesn't change in this situation does it?

 

[Delzac]

In this situation, n is constant, since they are not pumping more air, but instead, increasing the temperature of the air inside. So yeah. nR is in fact constant, for this question.