Question

The total internal energy of 4 moles of a diatomic gas at a temperature of \(27^\circ C\) is: (Universal gas constant \( R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1} \))

• A. \(13.47 \, \text{kJ}\)
• B. \(4.98 \, \text{kJ}\)
• C. \(24.93 \, \text{kJ}\)
• D. \(14.96 \, \text{kJ}\)

Hint:

For diatomic gases, the internal energy is calculated using \( U = \frac{5}{2} n R T \) because of the degrees of freedom.

Answer 1

The Correct Option is C

The internal energy of a diatomic gas is given by: \[ U = \frac{5}{2} n R T \] where: - \( n = 4 \) (number of moles), - \( R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1} \) (universal gas constant), - \( T = 27 + 273 = 300 \) K (temperature in Kelvin). \[ U = \frac{5}{2} \times 4 \times 8.31 \times 300 \] \[ U = 24.93 \, \text{kJ} \]