Concept of heating gas on pressure.

[chewchun]

I'm a little confused.

Lets say i have a rigid,non-expandable container.

If i heat the container,the gas molecules gain Kinetic energy.
I initially learned that the gas molecules will hit the wall with a larger force,hence larger pressure.But F=MA,so the gas molecules are accelerating?But what if they are not accelerating(high temperature,but not increasing temperature)?

I later learned that it is the increase in number of frequent effective collision per unit time with the wall.But Pressure=Force/Area. So there is a relationship between force and frequency??

 

[haruspex]

A molecule is accelerated every time it bounces off a wall. The greater its speed the greater that acceleration. Best to think of it in terms of momentum. Each bounce (on average) gives an impact proportional to the speed. As you say, the rate of impacts also increases with speed, so the pressure grows as the square of the speed. This is consistent with the fact that the kinetic energy per molecule grows with square of speed, and the temperature is a measure of the energy per (state per) molecule.

 

[CWatters]

chewchun..

Acceleration is defined as a change of velocity. Velocity, unlike speed, has a directional components... So changing direction = changing velocity = acceleration.

 

[CWatters]

I later learned that it is the increase in number of frequent effective collision per unit time with the wall.But Pressure=Force/Area. So there is a relationship between force and frequency??

Clearly. A rapid fire machine gun is more destructive than a single shot rifle. More bullets per second on target.

Each particle applies an impulse to the wall as it bounces off. An impulse is defined as the force multiplied by the time over which it occurs. In the case of molecules bouncing off the wall of a box the "time over which it occurs" is the interval between impacts.

Perhaps see
http://zonalandeducation.com/mstm/p...um/introductoryProblems/momentumSummary2.html

 

[jbriggs444]

Each particle applies an impulse to the wall as it bounces off. An impulse is defined as the force multiplied by the time over which it occurs. In the case of molecules bouncing off the wall of a box the "time over which it occurs" is the interval between impacts.

I think I see where you were going with this, but to me it reads misleadingly.

Each particle applies an impulse to the wall as it bounces off. Impulse is defined as the force multiplied by the time over which it occurs. The "time over which it occurs" for the impulse delivered by a particular molecule is the duration of the impact of that molecule with the wall, not the interval until the next impact. That figure is, of course, not very relevant.

pressure = force / area

force = momentum-delivered / time-taken-to-deliver-it

momentum-delivered = momentum-delivered-per-impact
* impacts-per-unit-time-per-unit-area
* time-taken-to-deliver-it
* area

Accordingly...

pressure = impacts-per-unit-time-per-unit-area * momentum-delivered-per-impact

 

[CWatters]

I think I see where you were going with this, but to me it reads misleadingly.

Each particle applies an impulse to the wall as it bounces off. Impulse is defined as the force multiplied by the time over which it occurs. The "time over which it occurs" for the impulse delivered by a particular molecule is the duration of the impact of that molecule with the wall, not the interval until the next impact.

Ah well yes ok but it makes no difference if you assume a high force/short duration or a low force/long duration impact. What matters is the area under the curve if you get what I mean.