How Does Rapid Compression Affect Gas Pressure and Temperature?

[beginner49]

HI all

I am glad to join your community.

Just thinking on this and I do not encounter a solution:

We have gas (1 litre of air, for example) in a cylinder at 1 atm pressure and 20ºC.

Then we compress this gas using a piston very quickly (there is no time enough to dissipate any heat out) down to 0.2 litre.

I assume that now we get a pressurized gas at 5 atm, and this gas temperature has also increased a lot.

My question is:

Is this new pressure higher than those 5 atm due to the fact that the higher temperature is a gas the larger volume it occupies?

Considering air as an ideal gas and there has not been any heat dissipated, what would be this pressure and temperature after compressing it down to 1/5 of its initial volumen?

Thanks.

 

[Redbelly98]

Welcome to PF

My question is:

Is this new pressure higher than those 5 atm due to the fact that the higher temperature is a gas the larger volume it occupies?

Pressure is higher than 5 atm due to the temperature being higher. The temperature is higher because compressing the gas quickly adds energy to it.

Considering air as an ideal gas and there has not been any heat dissipated, what would be this pressure and temperature after compressing it down to 1/5 of its initial volumen?

Thanks.

This can be worked out. Instead of PV=constant, as you have for a constant-temperature process, we have

PV ^γ = constant​

with γ=7/5 for air. That will give you the final pressure, and then you can get the temperature from the ideal gas law knowing P and V.

 

[beginner49]

Clear enough, Redbelly98

Thank you very much

 

[jtbell]

This is called an adiabatic process, by the way:

http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/adiab.html

 

[sardar]

I can provide a response to your question about pressure, volume, and temperature. First, let's review the relationship between these variables in an ideal gas. According to the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature. This equation shows that pressure and volume are inversely proportional, meaning that as one increases, the other decreases, as long as the other variables remain constant. Similarly, temperature and volume are directly proportional, meaning that as one increases, the other also increases, as long as the other variables remain constant.

In your example, you have compressed the gas from 1 litre to 0.2 litre, which means the volume has decreased by a factor of 5. According to the ideal gas law, this would result in an increase in pressure by a factor of 5, assuming all other variables remain constant. However, you also mention that the temperature has increased a lot due to the rapid compression. This means that the temperature is no longer constant, which will affect the pressure.

To accurately calculate the new pressure and temperature, we would need to know the initial temperature of the gas and the amount of heat that was added during compression. Without this information, it is difficult to determine the exact values. However, we can make some general statements based on the ideal gas law.

If we assume that the temperature is constant, then the pressure would indeed increase to 5 atm after compressing the gas to 0.2 litre. However, if the temperature increases, the pressure would also increase, possibly exceeding 5 atm. This is because as the temperature increases, the gas molecules have more energy and move faster, resulting in more collisions with the walls of the container and therefore a higher pressure.

To accurately determine the new pressure and temperature, we would need to use the ideal gas law and consider the change in temperature during compression. I hope this helps answer your question. Good luck with your research!