Thermal Physics - Gas Problems:

In summary, 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.
  • #1
Peter G.
442
0
Hi :smile:

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 105[/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.
 
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  • #2
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, NA? 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
 
  • #3
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.
 
  • #4
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
 
  • #5
Thanks for your answers
 

FAQ: Thermal Physics - Gas Problems:

What is thermal physics and how does it relate to gas problems?

Thermal physics is the branch of physics that studies the behavior of matter at a microscopic level, specifically in relation to temperature and heat. Gas problems involve analyzing the properties of gases, such as pressure, temperature, and volume, using principles from thermal physics.

What are the basic laws and equations used in thermal physics to solve gas problems?

The basic laws used in thermal physics are the ideal gas law, which relates pressure, volume, and temperature of an ideal gas, and the laws of thermodynamics, which describe the transfer of heat and work in a system. The equations used include the specific heat capacity equation and the equation for calculating the change in internal energy.

What is the difference between an ideal gas and a real gas?

An ideal gas is a hypothetical gas that follows the ideal gas law under all conditions. It has particles with no volume and no intermolecular forces. A real gas, on the other hand, does not always follow the ideal gas law and has particles with volume and intermolecular forces that affect its behavior.

How do you calculate the change in temperature, pressure, or volume of a gas in thermal physics?

The change in temperature, pressure, or volume of a gas can be calculated using the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of temperature and moles of gas. Additionally, the laws of thermodynamics can be used to calculate changes in temperature and pressure in a system.

What are some real-world applications of thermal physics in relation to gas problems?

Thermal physics and gas laws have many practical applications, such as in the design of engines, refrigeration systems, and air conditioning units. They are also used in weather prediction and understanding the behavior of gases in industrial processes. Additionally, thermal physics is crucial in the study of climate change and global warming.

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