Recall what entropy depends on

Entropy $S$ is a state function. For a given system, its value depends on the thermodynamic state, and hence it generally depends on variables such as temperature, pressure, volume, etc.

Therefore, in general, $S = S(T, P) \quad \text{or} \quad S = S(T, V)$ so $S$ is a function of temperature.

Check whether entropy change $\Delta S$ depends on temperature

Entropy change between two states is $\Delta S = \int \frac{\delta q_{\text{rev}}}{T}$

For example, for heating a substance from $T_1$ to $T_2$ at constant heat capacity, $\Delta S = nC \ln\left(\frac{T_2}{T_1}\right)$

This clearly shows that $\Delta S$ depends on temperature (through $T_1$ and $T_2$).

So $\Delta S$ is also a function of temperature.

Evaluate each option

• A: $S$ is a function of temperature but $\Delta S$ is not a function of temperature.
  False, because $\Delta S$ generally depends on temperature.

• B: Both $S$ and $\Delta S$ are not functions of temperature.
  False, because both generally depend on temperature.

• C: Both $\Delta S$ and $S$ are functions of temperature.
  True.

• D: $S$ is not a function of temperature but $\Delta S$ is a function of temperature.
  False, because $S$ does depend on temperature.

Final answer

The true statement is: $\boxed{\text{C}}$