At the beginning of the trip, we know:
Pressure P1 = 2.84x10^5 Pa
Temperature T1 = 281 K
At the end of the trip, we know:
Pressure P2 = 3.03x10^5 Pa
Temperature T2 = Unknown
We are also told to ignore expansion of the tires. This means The volumes V1 and V2 are the same.
From our gas law equation PV= nRT, the volume V is not changing, the number of moles n is not changing (if the tire is sealed then the particles of gas cannot escape), and R is a constant. We only care about P and T, so we should be them on the same side of the equation to see their relationship.
PV = nRT Divide by V on both aides
/V /V
P = nRT/V Divide by T on both sides
/T /T
P/T = nR/V Remember n,R, and V are being held constant
P/T = constant
P and T have a direct relationship and will always change in the same way so that the fraction of P/T always remains the same. (If P goes up, T goes up, and if P goes down, T goes down)
Even when the gas changes pressure or temperature, this fraction remains the same. This is called Gay-Lussac‘a Law:
P1/T1 = P2/T2
We will plug in what we have for P1, T1, and P2 and solve for T2 (T HAS TO BE IN KELVIN IN ORDER TO GO INTO ANY OF THE GAS LAW EQUATIONS)
(2.84x10^5)/(281) = (3.03x10^5)/T2
1010.67616 = (3.03x10^5)/T2 (don’t round, keep number in calculator)
Right now T2 is in the denominator so we will need to multiply both sides by T2 in order to get it out of the denominator. This makes T2 appear on the left side and disappear on the right side.
1010.67616 xT2 = 3.03x10^5 Lastly, divide both sides by 1010.67616
T2 = 299.799K Now we will check out significant digits and round the answer. The original given values have 3 significant digits so we will round to 3. (Look at 299–>the .7 tells us that 299 is going to round up to 300 kelvin)
T2 = 300. K
*You need to have a decimal point at the end of the number 300 like I have shown or you need to put a small horizontal line above the last 0 to indicate that these 0 digits are significant.*
