I think I'm doing this wrong
In an internal combustion engine, air at atmospheric pressure and a temperature of about 20 degrees celcius is compressed in the cylinder by a piston to 1/9 of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm
ok I'm using 1 atm to be 1.013E5 Pa
I'm using this formula
(P1 V1)/T1 = (P2 V2)/T2
all numbers subscripts
rearanged for T2
T2 = (T1 P2 V2)/(P1 V1)
T2 = ( 293 degrees K * 4.052E6 Pa * (1/9) )/ ( 1.013E5 Pa * 9)
I think the whole compression ratio thing screwed me up...
I think you just need to put v2 as (1/9)v1. v1 should just remain as v1. Then you can cancel out the v1 in the equation.
You are on the right track with using the Ideal Gas Law equation, but I can help you refine your approach and solve the problem accurately.
The Ideal Gas Law equation you mentioned is generally applicable, but in this case, we need to account for the compression ratio and the change in volume.
First, let's find the final volume (V2). We know that the compressed volume is 1/9 of the original volume, so if the original volume is V1, then V2 is (1/9) * V1.
Next, let's find the final pressure (P2). We are given that the pressure reaches 40 atm.
Now, let's substitute the values into the equation:
(T1 * P1 * V1) = (T2 * P2 * V2)
Since we are trying to solve for T2, rearranging the equation, we get:
T2 = (T1 * P1 * V1) / (P2 * V2)
Now, substitute the known values:
T2 = (293 K * 1.013E5 Pa * V1) / (40 atm * (1/9) * V1)
V1 cancels out, and the units need to be properly converted:
T2 = (293 K * 1.013E5 Pa) / (40 * 1.013E5 Pa * (1/9))
Now, simplify the equation further:
T2 = (293 K) / (40 * (1/9))
T2 = 293 K / (40/9)
T2 = 293 K * (9/40)
T2 = 66.21 K
So, the estimated temperature of the compressed air is approximately 66.21 Kelvin.
Keep in mind that this is an estimate. Actual engine conditions may vary due to factors such as heat transfer, internal friction, and combustion.