The Molar Heat Capacity for an Ideal Monatomic Gas

What is the relationship between Cp (molar heat capacity at constant pressure) and Cv (molar heat capacity at constant volume) for an ideal monatomic gas? Final answer: The molar heat capacity at constant pressure (Cp) is equal to the molar heat capacity at constant volume (Cv) for an ideal monatomic gas.

Explanation:

For an ideal monatomic gas, the molar heat capacity at constant pressure (Cp) is equal to the molar heat capacity at constant volume (Cv). This means that Cp = Cv.

However, it's important to note that Cp and Cv are not absolute values but rather depend on the specific gas and the conditions. For any ideal gas, Cp is greater than Cv for a given temperature and pressure. This relationship can be derived from the ideal gas law and the concept of internal energy.

But for an ideal monatomic gas, the relationship is such that Cp = Cv. This distinction is due to the simplified nature of a monatomic gas, which only has one atom per molecule and therefore exhibits different thermodynamic properties compared to other gases.

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