The total internal energy of two mole monoatomic ideal gas at temperature $$T = 300$$ K will be ______ J. (Given $$R = 8.31$$ J mol$$^{-1}$$ K$$^{-1}$$)

We need to find the total internal energy of two moles of a monoatomic ideal gas. The number of moles is $$n = 2$$, the temperature is $$T = 300$$ K, and the gas constant is $$R = 8.31$$ J mol$$^{-1}$$ K$$^{-1}$$. For a monoatomic ideal gas, the degrees of freedom $$f = 3$$, so the internal energy is given by:

$$U = \frac{f}{2} nRT = \frac{3}{2} nRT$$

Substituting the values:

$$U = \frac{3}{2} \times 2 \times 8.31 \times 300$$

$$U = 3 \times 8.31 \times 300$$

$$U = 3 \times 2493$$

$$U = 7479 \text{ J}$$

Hence, the total internal energy is 7479 J.