An alloy has a steady-state creep rate that follows ε̇ = Aσⁿexp(−Q/RT) with an activation energy of Q = 300 kJ/mol. If the temperature is raised from 1000 K to 1050 K at the same stress, by roughly what factor does the steady-state creep rate increase? Take R = 8.314 J/(mol·K).

Answer: C. About 5.6 times

The ratio of the rates is exp[(Q/R)(1/1000 − 1/1050)]. Since Q/R = 300000/8.314 ≈ 3.61×10⁴ K and (1/1000 − 1/1050) ≈ 4.76×10⁻⁵ K⁻¹, the exponent is about 1.72, and exp(1.72) ≈ 5.6 times. A rise of only 50 K increases the rate more than fivefold because the rate depends exponentially on temperature. The activation energy for high-temperature creep of pure metals is often close to that for self-diffusion, showing that creep is controlled by diffusion. About 52 times is the value obtained by treating the natural exponent as a power of 10, and about 1.05 times takes the ratio of the absolute temperatures as the ratio of the rates.