Problem — Internal energy of a monatomic gas

Problem

A container holds $n = 3{,}0$ moles of helium at $T = 350$ K. Calculate the internal energy of the gas (monatomic, $f = 3$).

Solution

For an ideal gas with $f$ degrees of freedom the internal energy is $U = \frac{f}{2}nRT$. For a monatomic gas $f = 3$: $U = \frac{3}{2}\,nRT$ $U = \frac{3}{2}\cdot 3{,}0 \cdot 8{,}31 \cdot 350$ $\ev{U \approx 1{,}31\cdot10^{4}\ \text{J}}$ The internal energy depends only on temperature (not on volume or pressure): it is the sum of the translational kinetic energy of all the molecules.

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Topics: Kinetic theory of gases Concepts: Internal energy · Temperature Skills: Micro-macro interpretation