[s.p.q.r]

Hi

When you compress a gas, its temperature increases. According to the ideal gas law, a gas' volume will be in direct proportion to its temperature.
So,
If you compressed air to the point where its temperature increased to 500 degrees C, would the compressed air then expand to assume the appropriate volume? (Assume that upon its expansion, it does not cool)

[Borek]

It this a constant volume (rigid contaner) experiment, or constant pressure (balloon, or rigid container with movable piston) experiment?

[s.p.q.r]

Hi

Thanks for your interest. It is at constant volume.

[Borek]

So the gas can't expand.

[s.p.q.r]

Yes, the gas cant expand. But its in a rigid container, so it will want to expand. Instead all energy will go to the molecules, so the molecules will have an increased internal energy.

Lets say that the air is 1 mole and has been compressed to 1 litre. Pretend this achives 500 degrees C.
If we do the ideal gas equation,

n-1
r-0.08206
t-773
v-1litre
p-    63.

So, the adiabatic compression of 1 mole(24 litres) into 1 litre, produces 500 degrees C, but will the gas, in its rigid container, increase in pressure to 63 bars (which would be in proportion to its temperature)?
 

[SudsMcDuff]

Yes, the gas cant expand. But its in a rigid container, so it will want to expand. Instead all energy will go to the molecules, so the molecules will have an increased internal energy.

Lets say that the air is 1 mole and has been compressed to 1 litre. Pretend this achives 500 degrees C.
If we do the ideal gas equation,

n-1
r-0.08206
t-773
v-1litre
p-    63.

So, the adiabatic compression of 1 mole(24 litres) into 1 litre, produces 500 degrees C, but will the gas, in its rigid container, increase in pressure to 63 bars (which would be in proportion to its temperature)?
 

Assuming the numbers above are correct, then yes, the temperature will increase along with the pressure. Keep in mind that P, V, and T are all inter-related by various equations. Increasing/decreasing just one often alters two variables.

The reason why we set things at "constant volume" (or sometimes constant temperature or pressure) is to analyze just 2 of the PVT variables and look at their proportionality. Otherwise, it'd be difficult. If I don't keep the volume and the pressure constant but I increase the temperature, then both V and P are going to change! And if P changes then V also changes! Tough to solve those compression-expansion problems when that happens. 

[s.p.q.r]

great

thanks alot.