Discussion
If the activation energy for relaxation is 30 KJ/mol, the relaxation time at 35°C will be
Answer: C
The relaxation time at 35°C is about 40.5 days.
For an Arrhenius process the relaxation time falls as temperature rises:
\[ \begin{aligned} \frac{\tau_{2}}{\tau_{1}} &= \exp\left[\frac{E_{a}}{R}\left(\frac{1}{T_{2}} - \frac{1}{T_{1}}\right)\right] \\ &= \exp\left[\frac{30000}{8.314}\left(\frac{1}{308.15} - \frac{1}{298.15}\right)\right] \\ &= e^{-0.393} = 0.675 \end{aligned} \]
so \(\tau_{2} = 60 \times 0.675 = 40.5\) days. The faster molecular motion at 35°C relaxes the stress sooner. The other options either barely change the time or change it too much for a 10°C rise with this activation energy.
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