How Does Temperature Affect Tire Pressure?

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Temperature significantly affects tire pressure, as demonstrated by a scenario where air in a tire is compressed to 26% of its original volume while the temperature rises from 10.0°C to 32.0°C. The relevant equation used is p1V1/t1 = p2V2/t2, which requires temperatures to be in Kelvin. After calculations, the final tire pressure is estimated to be around 4.1 atm or 420 kPa. The discussion highlights the importance of considering both volume reduction and temperature changes when determining tire pressure. Accurate conversions and significant figures are essential for precise results.
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Homework Statement


An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 26.0% of its original volume and the temperature is increased to 32.0°C.
(a) What is the tire pressure?


Homework Equations



p1V1/t1=p2v2/t2

The Attempt at a Solution


i know this is simple but I am just not getting the right answer I keep using p1V1/t1=p2v2/t2 but wrong answers come out. i used 1 atm for normal atmospheric pressure
 
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Remember that T must be in Kelvin since you are dividing by it.
 
yes it is in kelvin...i got 419903.5 is that right?
 
First estimate the answer!
Temperature hasn't changed much in absolute terms
volume has gone down by a factor of 4 - so we want a pressure of around 4 atm.

V1 = 1
V2 = 0.26
P1 = 1atm
T1 = 283K
P2 = ?
T2 = 305K

1/283 = 0.26 P /305
So P = (305 /283) / 0.26 = 4.1 atm or around 420KPa

ps. That's an impressive number of significant figures given the data!
 
it asks for it in pa that's y
 
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