# Thermal physics -- Converting the internal energy of argon atoms to temperature

• Kathhhriine
In summary, the conversation discussed using the equation U=3/2 NKbT to solve for temperature but getting different answers. The process for rearranging the equation and converting from mass to molecules was also mentioned. It was suggested to use a more accurate value for the Boltzmann constant to avoid rounding errors.
Kathhhriine
Homework Statement
The internal energy of 6.46 grams of argon is 568 J. What is the temperature of the argon atoms?
Relevant Equations
I tried using U=3/2 NKbT, but i dont seem to get the correct answer..
I tried using U=3/2 NKbT, but i don't seem to get the correct answer..

Please show us what answer you got and how you got it. Without this information we are as much in the dark as you are.

kuruman said:
Please show us what answer you got and how you got it. Without this information we are as much in the dark as you are.
I rearranged u=3/2NkbT, to get T=(2U)/(3NKb). Then i changed from mass to molecules, by taking N=(m/M)x(avogardos)=(6.46/39.9)x6.02x10^23=9.75x10^22. I plotted in the values; T=(2x568)/(9.75x10^22 x 1.3x10^-23 x3) =298K. The value given in the solution is 282K.

I got 281.4 K. I think you have a round-off error. Use the more accurate value ##k_B=1.38\times10^{23}~\mathrm{J/K}## for the Boltzmann constant.

BTW, Welcome to PF!

With an atomic mass of 39.95 u for Argon I got 281.8 K which rounds off to your given answer.

Binh Minh Duong, Kathhhriine and etotheipi
kuruman said:
I got 281.4 K. I think you have a round-off error. Use the more accurate value ##k_B=1.38\times10^{23}~\mathrm{J/K}## for the Boltzmann constant.

BTW, Welcome to PF!

With an atomic mass of 39.95 u for Argon I got 281.8 K which rounds off to your given answer.
Thank you!

## 1. How is the internal energy of argon atoms converted to temperature?

The internal energy of argon atoms can be converted to temperature by using the formula E = 3/2 * k * T, where E is the internal energy, k is the Boltzmann constant, and T is the temperature in Kelvin. This formula is based on the kinetic theory of gases, which states that the average kinetic energy of gas molecules is directly proportional to the temperature.

## 2. What is the relationship between internal energy and temperature in thermal physics?

In thermal physics, the relationship between internal energy and temperature is described by the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This means that as the internal energy of a system increases, the temperature also increases.

## 3. Can the internal energy of argon atoms be converted to temperature without adding or removing heat?

No, the conversion of internal energy to temperature requires the addition or removal of heat. This is because temperature is a measure of the average kinetic energy of particles in a system, and heat is the transfer of energy between two systems due to a temperature difference.

## 4. How does the mass of argon atoms affect the conversion of internal energy to temperature?

The mass of argon atoms does not directly affect the conversion of internal energy to temperature. However, the mass of the atoms can indirectly affect the temperature by changing the specific heat capacity of the gas. Heavier atoms have a higher specific heat capacity, which means they require more heat to increase their temperature compared to lighter atoms.

## 5. Is the conversion of internal energy to temperature the same for all types of gases?

No, the conversion of internal energy to temperature can vary depending on the type of gas. This is because different gases have different molecular structures and properties, which can affect the relationship between internal energy and temperature. However, the general principles of thermal physics still apply to all gases.

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