Celsius to Kelvin conversion problem (Kinetic theory)

  • Thread starter Forco
  • Start date
  • #1
Forco
6
0

Homework Statement


Find the temperature T that allows the rms speed of a gas to be equal to another gas with T=47°C.
The molecular mass of the first gas is 64, and the molecular mass of the second gas is 32.

Homework Equations


[tex]v_{rms}= \sqrt{\frac{3RT}{M}}[/tex]

The Attempt at a Solution


The problem is actually very easy. It's actually really simple to conclude that
[tex]T_1=2T_2[/tex]. However, my problem arises when actually replacing the given temperature.
If I take the second temperature to equal 47°C, then the first temperature is equal to 94°C. And converting that to kelvin gives 367.15 K.
However, if instead I use directly the temperature in K (47+273.15), then my answer becomes 640.3 K.
Which one is right? I assume the second one because in order for the equation to make sense, T needs to be expressed in K. I'd like to be sure, however.
 

Answers and Replies

  • #2
DrClaude
Mentor
8,135
4,959
The problem is actually very easy. It's actually really simple to conclude that
[tex]T_1=2T_2[/tex].
Well, that depends which gas you label 1, and which you label 2.

However, my problem arises when actually replacing the given temperature.
If I take the second temperature to equal 47°C, then the first temperature is equal to 94°C. And converting that to kelvin gives 367.15 K.
However, if instead I use directly the temperature in K (47+273.15), then my answer becomes 640.3 K.
Which one is right? I assume the second one because in order for the equation to make sense, T needs to be expressed in K. I'd like to be sure, however.
Think about this: what if the temperature was 0 °C instead of 47 °C.
 
  • #3
Forco
6
0
That would make the other temperature zero. Understood! Thank you very much.
 

Suggested for: Celsius to Kelvin conversion problem (Kinetic theory)

Replies
20
Views
2K
  • Last Post
Replies
11
Views
315
Replies
3
Views
2K
Replies
3
Views
412
Replies
5
Views
330
  • Last Post
Replies
3
Views
470
Replies
1
Views
283
Replies
14
Views
309
  • Last Post
Replies
3
Views
641
Top