What is the temperature of a monatomic ideal gas if 4 mol is known to be 820 kJ?

These problems: ν is the amount of matter of the taken monatomic ideal gas (ν = 4 mol); U – internal energy (U = 820 kJ = 82 * 10 ^ 4 J).

Const: R – univers. gas constant (R = 8.31 J / (mol * K))

To find out the temperature of the taken monatomic ideal gas, consider the formula: U = 1.5 * ν * R * Tx, whence we express: Tx = U / (1.5 * ν * R).

Let’s calculate: Tx = U / (1.5 * ν * R) = 82 * 10 ^ 4 / (1.5 * 4 * 8.31) ≈ 16446 K.

Answer: The temperature of the taken monatomic ideal gas, according to the calculation, is 16446 K.