Find the change of internal energy of the air.

AI Thread Summary
To find the change in internal energy of air in a car tire, the formula U=5/2nRT is used, considering air as a mixture of diatomic gases. The number of moles (n) is calculated using the ideal gas law, resulting in approximately 3.7 moles. After determining the final temperature from the pressure change, the internal energy is calculated to be around 2500 J, which aligns closely with the textbook answer of 2537 J when accounting for significant figures. The discussion emphasizes the importance of using the correct gas constant and significant figures in calculations. Overall, the calculations confirm the expected change in internal energy based on the given conditions.
MaiteB
Messages
44
Reaction score
0

Homework Statement


A car rubber has the volume 50 liters when it is bloated in a pressur 1.8 atm and in a temperature 293 K. After some hours of journey as an effect of friction the pressure will become 2atm. Find the change of internal energy of the air inside the rubber (U)

Homework Equations


U=3/2nRT

The Attempt at a Solution


I thought to sue the formula U=3/2nRT, but I don't know the n.
 
Physics news on Phys.org
Don't forget the ideal gas law. Also, in the formula for U, are you sure the fraction is 3/2? Nitrogen and oxygen are diatomic gases.
 
TSny said:
Don't forget the ideal gas law. Also, in the formula for U, are you sure the fraction is 3/2? Nitrogen and oxygen are diatomic gases.
Ok but how can I find the U with this compound of gases like air?
 
TSny said:
Don't forget the ideal gas law. Also, in the formula for U, are you sure the fraction is 3/2? Nitrogen and oxygen are diatomic gases.
I am writing my solution: pV=nRT=>n=(1.8*10^5*0.05)/(8.31*293)=3.7
1.8/293=2/x=>x=325.5555
U= 5/2* 3.7*8.31*(325.56-293)=2500, but in my book the answer is 2537J
 
Looks good. Some of the data in the problem is given to only 2 significant figures. So, the textbook should have rounded the answer to 2 significant figures which agrees with yours.
 
  • Like
Likes MaiteB
If you use 1.01325 x 105 for atm you find a better number. Your calculation is correct.
 
  • Like
Likes MaiteB

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Energy of a water tank with compressed air
Replies
5
Views
1K
Is enthalpy just the sum of internal energy and work against external pressure?
Replies
5
Views
985
Deriving an expression for change in internal energy
Replies
5
Views
1K
Internal Energy of an Ideal Gas
Replies
4
Views
2K
How Does Pressure Change Affect Internal Energy in an Ideal Gas?
Replies
4
Views
1K
Internal energy of a container filled with water & steam
Replies
12
Views
2K
Thermodynamics- Piston problem, pressure, internal energy
Replies
5
Views
2K
Internal energy during the expansion of a gas?
Replies
3
Views
2K
How Is Internal Energy Calculated for an Ideal Gas Using Temperature Change?
Replies
1
Views
1K
How Does Doubling Internal Energy Affect Pressure in a Sealed Container?
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top