Molecular interpretation of temperature

[thattgirljoyy]

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 v_rms 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

v_rms= √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

 

[NoPoke]

What happens to constants when you need a ratio?

 

[thattgirljoyy]

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

 

[I like Serena]

Welcome to PF, thattgirljoyy!

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...

Let's put it in formulas:
Before you have some unknown v_rms,before at 20 degrees Celsius, or 393 K.
Afterward you have v_rms,after=1.01v_rms,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?