How Does Constant Pressure Affect the Final RMS Speed of an Ideal Gas?

In summary, the conversation discusses finding the final rms speed of an ideal gas kept in a container of constant volume and pressure, with the initial rms speed given as 1800 m/s. The equation v(rms)=sqrt(3kT)/m is mentioned as a possible solution, but there is uncertainty about how to solve for the final rms speed without any given values for temperature. It is then suggested to use the equation PV=NkT=constant and rewrite it as (P1V1)/(P2V2)=T1/T2 to find the ratio of temperatures. However, there is confusion over whether the final and initial rms speeds should be equal, as they would be if v(rms,i)=v(rms,f
  • #1
map7s
146
0

Homework Statement


An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. If the initial rms speed is 1800 m/s, what is the final rms speed?


Homework Equations


v(rms)=square root of [v(avg)]^2=square root of (3kT)/m


The Attempt at a Solution


This was the only equation that I could find that dealt with rms speed, but the only problem is that I'm not sure how I can use just the initial rms speed to solve for the final rms speed with this equation.
 
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  • #2
Could it be a trick question? :wink:
 
  • #3
how would it be a trick question?
 
  • #4
Is anything changing? Is temperature changing? Have you given us the full question? If everything else is unchanged, then so is rms speed.
 
  • #5
And that's why I'd call it a trick question. Be sure you state the problem completely, just in case.
 
  • #6
I understand what you're saying now. The problem says that temperature and pressure are kept constant and to find the final rms speed. I tried entering in the same speed as the answer, but the program said that that was the wrong answer.
 
  • #7
My mistake...it says that volume and pressure are constant but it says nothing about temperature.
 
  • #8
I'd say 1800 * sqrt(Tfinal / Tinitial)
 
  • #9
the only problem is that the temperature is not given
 
  • #10
I sent my teacher an e-mail and he said, "First form the ratio of V_rms(ini)/V_rms(final), then you will see that
to find the ratio of the rms speeds what you need is the ratio of the
temperatures, which you can find using PV = NkT = constant" but I'm not sure how to figure out T w/o any values.
 
  • #11
map7s said:
I sent my teacher an e-mail and he said, "First form the ratio of V_rms(ini)/V_rms(final), then you will see that
to find the ratio of the rms speeds what you need is the ratio of the
temperatures, which you can find using PV = NkT = constant" but I'm not sure how to figure out T w/o any values.
If PV = NkT and all of P, V, N and k are constant, then what can you say about T?
 
  • #12
...it would have to be a constant too, right?
 
  • #13
Yes, it would.

In general, as long as the gas is in a closed container (no molecules can enter or escape, so N is fixed), you can rewrite the above equation as:

(P1V1)/(P2V2) = T1/T2

In this case, if P1=P2 and V1=V2, that leaves you with T1/T2=1
 
  • #14
so if I set it up as a ratio, like my teacher said, then it would be v(rms,i)/v(rms,f)=T1/T2=1
so v(rms,i)/v(rms,f)=1
so v(rms,i)=v(rms,f) right?
But that would mean that they would equal each other and I already plugged in that number and the program said that it wasn't correct.
 
  • #15
Either the program has it wrong, or you didn't write down the question correctly, or there's a typo in the question. Can't really say which it is.

Maybe the best you can do is take the above (corrected - see PS below) argument to your teacher, and find out where the problem is.

PS: There's a square root you're missing. v2/v1 = sqrt(T2/T1) - look at the equation you wrote down in the opening post.
 
Last edited:

Related to How Does Constant Pressure Affect the Final RMS Speed of an Ideal Gas?

1. What is the concept of root mean square (RMS) speed in an ideal gas?

The root mean square (RMS) speed of an ideal gas is the average velocity of gas particles in a system at a given temperature. It represents the speed at which the particles are moving on average, taking into account both their magnitude and direction.

2. How is the RMS speed of an ideal gas related to temperature?

The RMS speed of an ideal gas is directly proportional to the square root of its temperature. This means that as the temperature of the gas increases, the RMS speed of its particles will also increase.

3. What is the significance of the RMS speed of an ideal gas?

The RMS speed of an ideal gas is important because it helps us understand the behavior of gas particles in a system. It can provide information about the kinetic energy of the particles and their average speed, which is useful in predicting the properties and behavior of gases in different conditions.

4. How is the RMS speed of an ideal gas calculated?

The RMS speed of an ideal gas can be calculated using the formula: RMS speed = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. This formula takes into account the temperature and mass of the gas particles.

5. Does the RMS speed of an ideal gas change with pressure?

Yes, the RMS speed of an ideal gas is inversely proportional to the square root of its pressure. This means that as the pressure of the gas increases, the RMS speed of its particles will decrease. This is because as the gas particles are pushed closer together, they experience more collisions and have a lower average speed.

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