What is the temperature and mass of air in a tire after a change in pressure?

In summary, the tire's internal volume is 0.02m3 and has an initial pressure of 310 kPa at 15C. After a long run, the pressure rises to 340 kPa. To find the temperature of the air in the tire, the formula P2/P1 = T2/T1 is used, resulting in a temperature of 316.03 K. To calculate the mass of air that must be removed for the pressure to return to 310 kPa, the formula PV = nRT is used, with the molecular mass of air being 29 g/mol. The correct result is found to be 6.62g.
  • #1
chawki
506
0

Homework Statement


A car tyre with an intemal volume of 0,02m3 is filled to a pressure of 310 kPa at 15C.
After a long run, the pressure rises to 340 kPa.

Homework Equations


a) What is the temperature of the air in the tyre, assuming that the volume of the tyre is unchanged?
b) What mass of air must be removed for the pressure to retum to 310 kPa ? Take the
molecular mass of molecules in air to be 29 g/mol

The Attempt at a Solution


a) volume unchanged, means: P2/P1 = T2/T1
340000/310000 = T2/(273.15+15)
T2 = 316.03 K.

b) PV = nRT = (mRT/M)
m = (P1*V*M)/R*T2
m = (310000*0.02*29)/(8.314*316.03)
m = 68.43g
 
Physics news on Phys.org
  • #2


Anyone replying?
 
  • #3


chawki said:

Homework Statement


A car tyre with an intemal volume of 0,02m3 is filled to a pressure of 310 kPa at 15C.
After a long run, the pressure rises to 340 kPa.

Homework Equations


a) What is the temperature of the air in the tyre, assuming that the volume of the tyre is unchanged?
b) What mass of air must be removed for the pressure to retum to 310 kPa ? Take the
molecular mass of molecules in air to be 29 g/mol

The Attempt at a Solution


a) volume unchanged, means: P2/P1 = T2/T1
340000/310000 = T2/(273.15+15)
T2 = 316.03 K.

b) PV = nRT = (mRT/M)
m = (P1*V*M)/R*T2
m = (310000*0.02*29)/(8.314*316.03)
m = 68.43g

Your work looks okay to me. Do you know if it is correct?
 
  • #4


It would appear that you've calculated the total mass of the air required in the tire at the higher temperature, rather than the amount of air that must be removed to reach that total.
 
  • #5


I think it should be correct.
 
  • #6


gneill said:
It would appear that you've calculated the total mass of the air required in the tire at the higher temperature, rather than the amount of air that must be removed to reach that total.

ahhhh i think you're right.
maybe we should calculate the mass required for 340kpa and for 310kpa, and then the difference of those masses is the mass to be removed ?
 
  • #7


gneill said:
It would appear that you've calculated the total mass of the air required in the tire at the higher temperature, rather than the amount of air that must be removed to reach that total.

Thanks for catching that, gneill.
 
  • #8


m2=340000*0.02*29/8.314*316.03
m2=75.05g

m=310000*0.02*29/8.314*316.03
m=68.43g

75.05-68.43=6.62g and that's the mass we must remove to get 310000Pa ?
 
  • #9


Looks reasonable.
 
  • #10


Thank you gneill.
 

Related to What is the temperature and mass of air in a tire after a change in pressure?

1. What is the ideal temperature for air in a tire?

The ideal temperature for air in a tire is the same as the surrounding air temperature, typically between 70-90 degrees Fahrenheit. This allows the tire to maintain proper pressure and function efficiently.

2. Can the temperature of air in a tire affect its performance?

Yes, the temperature of air in a tire can greatly affect its performance. If the air is too cold, the tire may lose pressure and decrease fuel efficiency. If the air is too hot, the tire may expand and potentially lead to a blowout.

3. How does the temperature of air in a tire change during driving?

As a tire rolls on the road, friction causes the temperature of the air inside to increase. This is known as the "tire heat buildup" and can raise the temperature of the air by 50-60 degrees Fahrenheit.

4. What should I do if I notice a significant change in tire pressure due to temperature?

If you notice a significant change in tire pressure due to temperature, it is important to adjust the pressure accordingly. As a general rule, for every 10 degree change in temperature, tire pressure will change by 1 psi.

5. Does the temperature of air in a tire affect its lifespan?

Yes, the temperature of air in a tire can affect its lifespan. Extreme temperatures can cause the rubber in the tire to deteriorate faster, leading to a shorter lifespan. It is important to keep tires properly inflated and avoid extreme temperature changes to prolong their lifespan.

Similar threads

Thermal physics problem -- Pressure and temperature of air in a refrigerator
    • Introductory Physics Homework Help
Replies
2
Views
4K
What helium mass in a balloon to make it bouyant in air?
    • Introductory Physics Homework Help
Replies
12
Views
657
Calculating Tire Pressure Change with Temperature Increase
    • Introductory Physics Homework Help
Replies
2
Views
1K
Engineering Calculating the mass of air in a pressurised air tank
    • Engineering and Comp Sci Homework Help
Replies
14
Views
1K
The mass of air in the pressurised air tank
    • Introductory Physics Homework Help
Replies
31
Views
4K
Using Pressure and Temperature differences to find height
    • Introductory Physics Homework Help
Replies
3
Views
2K
Temperature after closing the valve
    • Engineering and Comp Sci Homework Help
Replies
8
Views
1K
What is the formula for calculating the mass of air in a piston?
    • Introductory Physics Homework Help
Replies
6
Views
1K
What are the steps to solve a polytropic process problem?
    • Introductory Physics Homework Help
Replies
6
Views
2K
A Temperature and pressure change in an air vessel
    • Thermodynamics
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top