Molecular interpretation of temperature

In summary, the speaker is struggling with their AP Physics summer work and is seeking guidance on how to use equations correctly. They are currently stuck on a question about vms and temperature. They also need help with a conceptual problem involving vrms, pressure, and density of a gas. The conversation also briefly touches on a question about constants and ratios.
  • #1
thattgirljoyy
2
0
i'm trying to do my ap physics summer work, but I've been having a hard time trying to teach this to myself. i do really well in class, but i need a little bit of guidance to help explain how to use the equations the right way.

i'm currently stuck on a question about vrms an it's relation to temp.

Homework Statement


the rms speed of molecules in a gas at 20degrees celsius is to be raised by 1%. To what temperature must it be raised?

Homework Equations


vrms= √3kT/m

The Attempt at a Solution


i don't have any clue where to start if it didn't give me the gas to find it's mass.-i was wondering if i could find someone who could maybe stay in touch for a day or two so i can reach out if i get stuck on anything
 
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  • #2
What happens to constants when you need a ratio?
 
  • #3
okay, the temperature would change by sqrt 2, right ?
essentially about 6 degrees kelvin.

i'm stuck on another problem, it seems to be more conceptual.
it says to prove how
vrms=√P/ρ
P, pressure
ρ, density of the gas

i started with the two equations
P=1/3Nmv^2/V
v^2=3KT/m

i assumed the goal was to get the V from the first equation into the denominator of the second to try to get the density (m/v)
some how all I've gotten to was
P/ρ=[3KT(1/3)N]/m

i'm trying to see if i can get the original 3KT/m to revert back to v^2, but i don't know how to get rid of the (1/3)N/m
 
  • #4
Welcome to PF, thattgirljoyy! :smile:

thattgirljoyy said:
okay, the temperature would change by sqrt 2, right ?
essentially about 6 degrees kelvin.

It's not too far off 6 degrees... but there is no sqrt 2 involved that I can see... :confused:

Let's put it in formulas:
Before you have some unknown vrms,before at 20 degrees Celsius, or 393 K.
Afterward you have vrms,after=1.01vrms,before at some unknown temperature T.
Substitute and solve for T?
i'm stuck on another problem, it seems to be more conceptual.
it says to prove how
vrms=√P/ρ
P, pressure
ρ, density of the gas

i started with the two equations
P=1/3Nmv^2/V
v^2=3KT/m

i assumed the goal was to get the V from the first equation into the denominator of the second to try to get the density (m/v)
some how all I've gotten to was
P/ρ=[3KT(1/3)N]/m

i'm trying to see if i can get the original 3KT/m to revert back to v^2, but i don't know how to get rid of the (1/3)N/m

Did you consider that m is the mass of one molecule?
What is the mass of all molecules in the volume V?
 
  • #5
Hello!

I understand that learning new concepts can be challenging, especially when trying to teach yourself. I am happy to provide some guidance and clarify any questions you may have about the molecular interpretation of temperature.

First, let's review the definition of temperature. Temperature is a measure of the average kinetic energy of the molecules in a substance. In other words, it is a measure of how fast the molecules are moving. This means that as temperature increases, the average speed of the molecules also increases.

Now, let's look at the equation you provided for vrms. This equation relates the root mean square (rms) speed of molecules (vrms) to the temperature (T) and the mass of the molecules (m). The constant, k, is known as the Boltzmann constant and has a value of 1.38 x 10^-23 J/K. This equation tells us that as the temperature increases, the vrms of the molecules also increases.

Now, let's apply this to the question you are stuck on. The question asks you to raise the vrms of molecules in a gas at 20 degrees Celsius by 1%. This means we need to find the new temperature, T2, that will result in a 1% increase in vrms. We can set up an equation using the given information:

vrms2 = 1.01 * vrms1

Where vrms1 is the initial vrms at 20 degrees Celsius and vrms2 is the new vrms at the higher temperature we are trying to find.

Plugging in the equation for vrms, we get:

√3kT2/m = 1.01 * √3kT1/m

Where T1 is the initial temperature of 20 degrees Celsius.

We can solve for T2 by isolating it on one side of the equation and simplifying:

T2 = (1.01^2 * T1) = 1.0201 * T1

This means that the new temperature, T2, must be 1.0201 times the initial temperature, T1, in order to raise the vrms of the molecules by 1%.

I hope this helps you understand the relationship between vrms and temperature better. If you have any further questions, please feel free to reach out to me. I am happy to help you with your AP Physics summer work. Good luck!
 

1. What is the molecular interpretation of temperature?

The molecular interpretation of temperature is the measure of the average kinetic energy of the molecules in a substance. It is directly related to the speed at which the molecules are moving and their collisions with each other.

2. How does temperature affect molecular movement?

As temperature increases, the molecules in a substance gain more kinetic energy and move faster. This leads to an increase in molecular collisions and a greater amount of movement within the substance.

3. How is temperature related to the states of matter?

Temperature plays a crucial role in determining the state of matter of a substance. As the temperature increases, the molecules gain more energy and can overcome the intermolecular forces holding them together, causing a change in state from solid to liquid to gas.

4. Can temperature be negative in the molecular interpretation?

In the molecular interpretation, temperature is a measure of the average kinetic energy of molecules. It cannot be negative, as molecules cannot have negative energy. However, in some scales, such as the Kelvin scale, negative temperatures can be used to indicate that the molecules have a higher energy state than at positive temperatures.

5. How does temperature affect chemical reactions at the molecular level?

Temperature has a significant impact on chemical reactions at the molecular level. As temperature increases, the molecules gain more kinetic energy and move faster, leading to an increase in the rate of collisions and a higher likelihood of successful reactions. Temperature also affects the activation energy required for a reaction to occur, with higher temperatures lowering the activation energy barrier and making the reaction more favorable.

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