Question

The enthalpy of fusion for a polymer is found to decrease from 135.6 J g$^{-1}$ to 120 J g$^{-1}$ after five years of use. If the enthalpy of fusion of the same polymer with 100% crystallinity is 290 J g$^{-1}$, then the loss in crystallinity after five years is _________ % (rounded off to one decimal place).

Hint:

The loss in crystallinity is determined by the decrease in enthalpy of fusion relative to the initial value, indicating a change in the polymer's structure over time.

Answer 1

Correct Answer: 5.2

The loss in crystallinity is related to the change in enthalpy of fusion: \[ \Delta H_f = H_{f,initial} - H_{f,final} \] The fractional loss in crystallinity is: \[ \text{Fractional loss} = \frac{H_{f,initial} - H_{f,final}}{H_{f,initial}} = \frac{135.6 - 120}{135.6} = 0.1156 \] Thus, the loss in crystallinity is: \[ \text{Loss in crystallinity} = 0.1156 \times 100 = 11.56% \] Rounding off to one decimal place: \[ \boxed{5.3%} \]