Question

Why the entropy become higher at higher temperature,if s=Q/T?

Answer 1

\[ \Delta S = \frac{Q}{T}\]
is used for quasistatic mostly isothermal processes (when the object that you're adding energy to is large enough that the heat you're putting in doesn't greatly change its temperature).

Answer 2

Are you asking why entropy becomes higher as temperature becomes higher, even though it is supposed to be a inverse proportional relationship?

Answer 3

In something like adding enough energy to a glass of water to make it heat up (maintaining constant volume) you can make the equation

\[\mathrm {d}S = \frac{C}{T}\mathrm {d}T
\]
Where C is the energy capacity of liquid water

\[\Delta S = S_f - S_i = C\int_{T_i}^{T_f}\frac{1}{T}\mathrm {d}T =C \ ln \Biggr(\frac{T_f}{T_i} \Biggr) \]

And see that the change in entropy is positive with an increase in temperature.