Root mean square velocity question

In summary, the conversation discusses the relationship between temperature, pressure, and root mean square (r.m.s) velocity. The formula Vrms = √(3P/density) is mentioned and it is stated that there is also a direct relation between pressure and temperature (PV = nRT). The conversation ends with a suggestion to use these equations to relate r.m.s velocity with temperature through algebraic manipulation.
  • #1
Insiya
7
0
If at 120 K the Vrms is v , then at 480 K it will be

a. 1
b. 2
c. 3
d. 4
Which formula is to be used here? Plz solve this.
 
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  • #2
We don't solve anything here. We can help, but only if you show some effort.
 
  • #3
Ok.. but I couldn't understand it.. The formula mentioned in my book is Vrms= radical 3P/density so...What to do next?
 
  • #4
Are you saying there is no equation linking r. m. s. velocity and temperature that you know of?
 
  • #5
No.. I am not saying this.. This formula also shows relation with temperature but how to continue..?
 
  • #6
Perhaps you could express how pressure depends on temperature?
 
  • #7
Pressure has direct relation with temperature
 
  • #8
What is the equation?
 
  • #9
PV=nRT
 
  • #10
Use this and the equation given for r. m. s. velocity to relate the latter with T.
 
  • #11
Any clue?
 
  • #12
The clue is in #10. The rest is just algebra.
 
  • #13
ok.. Thank U
 

1. What is root mean square velocity?

Root mean square velocity, commonly referred to as RMS velocity, is a mathematical measure of the average speed of molecules or particles in a gas or liquid. It is calculated by taking the square root of the average of the squared velocities of all the particles.

2. How is root mean square velocity different from average velocity?

Average velocity is a simple measure of the average speed of particles in a gas or liquid, while root mean square velocity takes into account the distribution of velocities and provides a more accurate measure of the average speed.

3. What factors affect the root mean square velocity of particles?

The root mean square velocity of particles is affected by temperature, molecular weight, and the type of gas or liquid. As temperature increases, the root mean square velocity also increases. Heavier molecules have lower root mean square velocities compared to lighter molecules at the same temperature. The type of gas or liquid also plays a role in the root mean square velocity, as different types of gases and liquids have different molecular weights and properties.

4. How is root mean square velocity related to kinetic energy?

Root mean square velocity is directly proportional to the kinetic energy of particles. As the root mean square velocity increases, so does the kinetic energy. This means that at higher temperatures, particles have higher root mean square velocities and therefore, higher kinetic energies.

5. What is the significance of root mean square velocity in scientific research?

Root mean square velocity is an important concept in various areas of scientific research, including thermodynamics, fluid mechanics, and atmospheric science. It provides a more accurate measure of the average speed of particles in a gas or liquid, which is necessary for understanding the behavior and properties of these substances.

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