What is the new pressure in a bicycle tire after riding on a hot day?

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SUMMARY

The new pressure in a bicycle tire after riding on a hot day can be calculated using the ideal gas law, PV=NRT. Initially, the tire pressure is 68 psi at 28°C. After the temperature increases to 58°C and the volume expands by 3.9%, the new pressure is approximately 6.89 psi. However, this calculation is incorrect as it does not account for the relationship between pressure, volume, and temperature properly. The correct approach involves using the combined gas law to find the new pressure directly.

PREREQUISITES
  • Understanding of the ideal gas law (PV=NRT)
  • Knowledge of unit conversions (psi to pascals)
  • Familiarity with temperature conversion (Celsius to Kelvin)
  • Basic principles of gas behavior under varying conditions
NEXT STEPS
  • Study the combined gas law for pressure-volume-temperature relationships
  • Learn about unit conversions between psi and pascals
  • Explore the effects of temperature on gas pressure in closed systems
  • Practice solving problems involving gas laws with real-world applications
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Students studying physics or engineering, particularly those focusing on thermodynamics and gas laws, as well as anyone interested in understanding the behavior of gases under varying conditions.

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Homework Statement


A bicycle tire is filled with air to a pressure of 68 psi, at a temperature of 28°C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58°C. The volume of the tire increases by 3.9%. What is the new pressure in the bicycle tire?



Homework Equations


PV=NRT


The Attempt at a Solution


Well... I went through it first by changing psi into pascals, then celsius into Kelvin. then I made an attempt to find volume which I got 5.9736e-4 for. ( i kind of ignored the moles because I ddidn't know what to do with it, so I put it in as 1 to pretty much negate it) then I multiplied the volume by 1.039 and plugged in the R constant and 359.15 K to try to find pascals. which I got 47484.6921 Pascals, but it asked for answers in psi, so I tried to switch it to psi by dividing by 6894.8 and got 6.89 psi. I don't think this is even close to right.
 
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Your main quantities are P, V, T. The quantities of n and R are not needed. Neither of these last two would change. Do you remember how P, V, and T by themselves are related?
 
PV= T right?
 

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