Celsius to Kelvin conversion problem (Kinetic theory)

In summary, the problem involves finding the temperature T that will make the root mean square speed of a gas with molecular mass 64 equal to the root mean square speed of a gas with molecular mass 32 at a temperature of 47°C. The equation for root mean square speed is v_{rms}= \sqrt{\frac{3RT}{M}} and the question is which temperature to use for T. After some discussion, it is determined that T should be expressed in Kelvin, so the correct answer is 640.3 K.
  • #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.
 
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  • #2
Forco said:
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.

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.
 
  • #3
That would make the other temperature zero. Understood! Thank you very much.
 

1. What is the formula for converting Celsius to Kelvin?

The formula for converting from Celsius (°C) to Kelvin (K) is: K = °C + 273.15. This is because the Kelvin scale starts at absolute zero, which is -273.15 degrees Celsius. Therefore, to convert from one scale to the other, we simply need to add 273.15.

2. Why is Kelvin often used in the study of kinetic theory?

Kelvin is often used in the study of kinetic theory because it is the absolute temperature scale and does not have any negative values. In kinetic theory, temperature is directly related to the average kinetic energy of particles in a substance. Absolute zero, which is 0 K, represents the complete absence of any kinetic energy. This makes it a useful scale for studying the behavior of particles in gases, liquids, and solids.

3. How does the conversion from Celsius to Kelvin affect the value of temperature?

The conversion from Celsius to Kelvin does not change the value of temperature, but rather it represents the same temperature in a different scale. For example, 25 degrees Celsius is equivalent to 298.15 Kelvin. Both values represent the same temperature, just in different units.

4. Is the conversion from Celsius to Kelvin reversible?

Yes, the conversion from Celsius to Kelvin is reversible. This means that you can convert a temperature from Celsius to Kelvin and then back from Kelvin to Celsius and you will end up with the same value. This is because both scales use the same unit of measurement, the degree.

5. Can you convert any temperature from Celsius to Kelvin?

Yes, any temperature can be converted from Celsius to Kelvin, as long as it is within the range of possible values for both scales. However, it is important to note that temperatures below absolute zero (-273.15°C or 0 K) do not exist in the physical world and therefore cannot be converted between the two scales.

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