Change in entropy and its relation with temperature

[Helen Zhao 1F]

For problem 4F.3 from the 7th edition, why is there a greater change of entropy at a lower temperature?

[Vincent Li 4L]

Change in entropy can be calculated using the formula: deltaS = q / T. In this case, delta S is change in entropy, q is the heat of a reversible reaction, and T is absolute temperature. Mathematically speaking, the lower your temperature is, the greater delta S will be, thereby allowing a greater increase in entropy. Qualitatively speaking, at lower temperatures, the particles are moving around less, so an increase in temperature will cause the particles to move more frantically and increase disorder. Contrarily, at higher temperatures, the particles are already moving around due to having a higher average kinetic energy, so additional heat being imparted into the system makes less of a difference. Hope that helps.

[Jessica Castro 2H]

Looking at the equation for the change in entropy (delta S = q / T), we can see that temperature (T) is inversely related with the change in entropy (delta S). Therefore, at lower temperatures, there will be a greater change in entropy.
Looking at the concept of entropy conceptually, entropy changes as energy is used by the system at a constant temperature. At lower temperatures, more heat or energy is needed by the system, and therefore a bigger change in entropy will be produced.