Question

What happens to the entropy of the system when the temperature increases?

Answer 1

Hint: Temperature always affects the kinetic energy of particles and their random motion. A relationship between changing temperature and the zigzag motion of the particles indicates its effect on the entropy of the system being observed.

Complete answer:
Entropy denoted by $ S $ is a thermodynamic state function that measures the extent of randomness or disorder in a particular system under observation. A system with more chaos or particles moving in a disordered manner is said to have higher entropy and a system which has its particles arranged in an order is said to have lower entropy.
Naturally every system has a tendency to bring about a change that causes an increase in entropy as higher entropy is always preferred.
Temperature is a state variable that helps define the bulk properties of matter. Any change in temperature can bring about a corresponding change in the state of the system.
When a heat exchange takes place between the system and the surrounding, it causes a temperature change between the two (provided that the process is not isothermal in nature). An increase in temperatures raises the thermal energy (average kinetic energy) of the particles (atoms or molecules) present inside the system.
Particles with higher thermal (average kinetic) energies become capable of moving in random directions with higher velocities. Hence, temperature changes are directly related to entropy changes of a system and temperature is said to be the measure of average disordered motion of particles inside the system.
Thus, entropy of the system always increases with increases in temperature and vice versa.

Note:
The formula of entropy $ S = \dfrac{q}{T} $ has temperature in the denominator but it does not mean that an increase in the temperature independently decreases the entropy. Temperature changes also influence heat and one must not derive a direct relationship between entropy and temperature from the formula by ignoring the heat involved in the thermodynamic process.