Celsius to Kelvin conversion problem (Kinetic theory)

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SUMMARY

The discussion centers on converting temperatures from Celsius to Kelvin in the context of calculating the root mean square (rms) speed of gases. The equation used is v_{rms}= \sqrt{\frac{3RT}{M}}, where T must be in Kelvin. The confusion arises when determining the correct temperature for the first gas based on a second gas temperature of 47°C, leading to two different Kelvin values: 367.15 K and 640.3 K. The correct approach is to always convert Celsius to Kelvin before applying the equation, confirming that T must be expressed in Kelvin for accurate calculations.

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  • Understanding of the ideal gas law and kinetic theory
  • Familiarity with temperature conversion between Celsius and Kelvin
  • Knowledge of root mean square speed calculations
  • Basic algebra for manipulating equations
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  • Study the derivation of the rms speed formula v_{rms}= \sqrt{\frac{3RT}{M}}
  • Learn more about temperature scales and conversions, specifically Celsius to Kelvin
  • Explore the implications of molecular mass on gas behavior in kinetic theory
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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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