Thermal Physics - Gas Problems:

[Peter G.]

Hi

1. A car tyre has a volume of 18 x 10^-3 m³ and contains air at an excess pressure of 2.5 x 10⁵ N/m² above atmospheric pressure (1.0 x 10⁵ N/m²) Calculate the volume which the air inside would occupy at atmospheric pressure assuming that its temperature remains unchanged:

My attempt:

PV (Initial) = PV (Final)
(2.5 x 10⁵+1.0 x 10⁵) x 18 x 10^-3 / 1.0 x 10<sup>5[/SUP = V

V = 0.063 m3

2. An oxygen cylinder contains 0.50 kg of gas at a constant pressure of 0.50 MN/m2 and a temperature of 7 degrees Celsius. What mass of oxygen must be pumped into raise the pressure to 3.0 MN/m2 at a temperature of 27 degrees Celsius. If the molar mass of oxgen is 32 x 10-3 kg, calculate the volume of the cylinder

My attempt:

I know this probably can be done in a simpler way but...

First I found the volume with the initial conditions:

V = nRT / P
V = 15.625 x 8.31 x 280 / 500
V = 72.7125

then:

I changed n for mass / molar mass:

m / 32x10-3 = 3000 x 72.7125 / 8.31 x 300

m = 2.8

But since it is how much more oxygen must be pumpted:

m = 2.8-0.5
m = 2.3

Thanks in advance,
Peter G.

(P.S: I never learned moles and I know this question is a bit stupid but I am insecure: The molar mass of carbon dioxide is 44.0 x 10-3 kg. Calculate (a) the number of moles and (b) the number of molecules in 1 kg of the gas:)

I got 22.73 for both.</sup>

 

[mrmiller1]

Peter,

Everything looks good! I got the same numbers.

The only part I disagree with is in the last part for "(b) the number of molecules in 1 kg of the gas"
In 1 kg of CO₂ you will have a gigantic amount of molecules. Have you ever used a constant in class called Avogodro's Constant, N^A? This is will tell you how many molecules you will have per mole.

Since you mentioned you wern't familiar with moles...
mole = the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of the isotope carbon-12 [wikipedia]

Please let me know if you have any questions.

Mike
mrmiller1@mail.widener.edu

 

[Peter G.]

Thank you for your answer!

So, from what I understand, the number of molecules should really be the number of moles multiplied by Avogadro's Constant, correct?

But, if you wouldn't mind, could you help me with something else?

An adiabatic contraction means a decrease in the volume of a gas but without any thermal energy going in or out the system. I understand a gas heats up due to work being done on it. But how can the energy be transferred (work be done on the gas) if no thermal energy can enter or exit the system?

Thanks,
Peter G.

 

[mrmiller1]

The contractor or aka compressor's job is to compress the fluid. So while it is adiabatic, there is still work being used by the compressor to rotate its gears and vanes and in the process the pressure of the fluid is increased and the specific volume is decreased. If the energy enters the fluid via work then it is still considered adiabatic. This must happen or else the compressor wouldn't do anything. It would not be adiabatic anymore if, for example, the outside air around the compressor cooled down the processing fluid (fluid entering the compressor).

Mike

 

[Peter G.]

Thanks for your answers