Specific Heat Experiment with Monatomic Gas

How many degrees of freedom does an atom in this monatomic gas have?

In an experiment with a monatomic gas, the atom has three degrees of freedom. But why does it have only three?

Degrees of Freedom in Monatomic Gas

In this experiment with a monatomic gas, the atom has three degrees of freedom. The molar mass of the gas is approximately 83.48 g/mol, based on the specific heat of 0.149 J/gK.

In Part A, for a monatomic gas, each atom has only translational degrees of freedom.

According to the equipartition theorem, each degree of freedom contributes 1/2kT to the total energy, where k is the Boltzmann constant and T is the temperature.

For translational motion, there are three degrees of freedom in three dimensions. Therefore, an atom in this monatomic gas has three degrees of freedom.

In Part B, we can calculate the molar mass of the gas using the specific heat at constant volume (cV) value.

The molar heat capacity at constant volume (Cv) for a monatomic gas is given by Cv = (3/2)R, where R is the gas constant. Rearranging the equation, we have Cv = (3/2)R = (3/2)(8.314 J/mol·K) = 12.471 J/mol·K.

To find the molar mass (m) of the gas, we can use the equation m = Cv / cV. Substituting the values, we have m = 12.471 J/mol·K / 0.149 J/g·K.

Now, we need to convert grams to moles. The molar mass of the gas (m) can be expressed as m = (12.471 J/mol·K) / (0.149 J/g·K) × (1 mol / x g), where x is the molar mass of the gas in grams per mole.

By rearranging the equation, we find x = (12.471 J/mol·K) / (0.149 J/g·K) = 83.48 g/mol.

Therefore, the molar mass of the gas is approximately 83.48 g/mol.

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