Crystal defects and diffusion
The diffusion coefficient of carbon in γ-iron follows the Arrhenius form D = D₀exp(−Q/RT) with D₀ = 2.3×10⁻⁵ m²/s and activation energy Q = 148 kJ/mol. Which value is closest to the diffusion coefficient at 927 °C? Take the gas constant as R = 8.314 J/(mol·K).
- AAbout 8.3×10⁻¹² m²/s
- BAbout 1.1×10⁻¹³ m²/s
- CAbout 2.3×10⁻⁵ m²/s
Show answer and explanation
Answer: A. About 8.3×10⁻¹² m²/s
Convert the temperature to absolute temperature: T = 927 + 273 = 1200 K. Q/RT = 148000/(8.314 × 1200) ≈ 14.83, so D = 2.3×10⁻⁵ × exp(−14.83) ≈ 2.3×10⁻⁵ × 3.6×10⁻⁷ ≈ 8.3×10⁻¹² m²/s. About 1.1×10⁻¹³ is the mistake of substituting the temperature as 927 in °C. About 2.3×10⁻⁵ is the mistake of leaving Q as 148 in kJ, which makes the exponent nearly zero and gives almost the same value as D₀. Because D changes exponentially with temperature, raising the carburizing temperature by just a few tens of degrees can shorten the treatment time considerably.