Celsius to Kelvin conversion problem (Kinetic theory)

AI Thread Summary
To find the temperature T that equates the rms speed of two gases, the relationship T_1=2T_2 is established, where T_2 is 47°C. Converting 47°C to Kelvin yields 320.15 K, leading to T_1 being 640.3 K when calculated directly. However, if 47°C is converted to Celsius first, T_1 would be 367.15 K. The correct approach emphasizes that temperatures must be in Kelvin for the equation to be valid, confirming that 640.3 K is the accurate result. The discussion highlights the importance of consistent temperature units in calculations.
Forco
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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


v_{rms}= \sqrt{\frac{3RT}{M}}

The Attempt at a Solution


The problem is actually very easy. It's actually really simple to conclude that
T_1=2T_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.
 
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Forco said:
The problem is actually very easy. It's actually really simple to conclude that
T_1=2T_2.
Well, that depends which gas you label 1, and which you label 2.

Forco said:
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.
 
That would make the other temperature zero. Understood! Thank you very much.
 
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