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?
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.