Q138 / 160 · TS EAMCET 2024 (09 May Shift 1) · Physics

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

  • A
    13.47 kJ
  • B
    4.98 kJ
  • Correct answer
    C
    24.93 kJ
  • D
    14.96 kJ

Solution

Total internal energy $u=n \frac{f}{2} \mathbf{R T}$ for diatomic gas $\mathrm{f}=5, \mathrm{n}=4$ moles and $\mathrm{T}=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$ given Therefore $u=4 \times \frac{5}{2} \times 8.31 \times 300=24.93 \times 10^3 \mathrm{~J}$ or, $u=24.93 \mathrm{~kJ}$

Hence, the correct answer is option: 'C'.

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