1. For a monoatomic ideal gas, the total internal energy is

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

2. Given:

$n = 2\ \text{mol}, \quad R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}, \quad T = 300\ \text{K}$

3. Substitute into the formula:

$U = \frac{3}{2}(2)(8.31)(300)$

Since

$\frac{3}{2}\times 2 = 3$

we get

$U = 3 \times 8.31 \times 300$

4. Now calculate:

$8.31 \times 300 = 2493$

So,

$U = 3 \times 2493 = 7479\ \text{J}$

5. Therefore, the total internal energy is

$\boxed{7479\ \text{J}}$

Comparison with stored correct answer:

• Derived answer: $7479$
• Stored correct answer: $7479$

These match exactly.