# Internal energy of 10 moles of a monatomic ideal gas 600 J. What is the temperature of the gas?

September 20, 2021 | education

| Initial data: ν (number of moles of a monoatomic ideal gas) = 10 mol; U (internal gas energy) = 600 J.

Reference values: R (universal gas constant) = 8.31 J / (mol * K); i (the number of degrees of freedom of a monatomic ideal gas) = 3.

We express the temperature of a given monoatomic gas from the formula: U = i * ν * R * T / 2, whence T = 2U / (i * ν * R).

Let’s calculate: T = 2 * 600 / (3 * 10 * 8.31) = 4.81 K.

Answer: The temperature of a monatomic ideal gas will be 4.81 K.

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