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Chemistry · The first law of thermodynamics: Concept of work, heat, internal energy and enthalpy, heat capacity, molar heat capacity

When 229 J of energy is supplied as heat at constant pressure to 3 mol , \) the

When 229 J of energy is supplied as heat at constant pressure to 3 mol \( A r(g), \) the temperature of the sample is increased by \( 2.55 \mathrm{K} \). Calculate the motor heat capacity at constant volume:

  • A. 30 KJ \( K^{-1} \) mol \( ^{-1} \) -
  • B. 30 J K \( ^{-1} \) mol \( ^{-1} \)
  • C. 21.7 J K \( ^{-1} \) mol \( ^{-1} \)
  • D. 21.7 KJ K \( ^{-1} \) mol \( ^{-1} \)

Step-by-step solution

First, compute molar heat capacity at constant pressure: C_p,m = q / (nΔT) = 229 J / (3 mol × 2.55 K) ≈ 29.93 J mol⁻¹ K⁻¹. For an ideal gas, C_p,m - C_v,m = R, so C_v,m = C_p,m - R ≈ 29.93 - 8.314 = 21.62 J mol⁻¹ K⁻¹ ≈ 21.7 J mol⁻¹ K⁻¹. Thus, option C is correct.
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