The maximum Entropy

[kky]

By the second Law of Thermodynamics, we know the Entropy of the Universe always increases.
But we also know by the formula dS = d'Q/T that when we supply heat and increase the Entropy we also increase temperature. As for a given amount of heat the increase in entropy is smaller at a higher temperature than at a lower temperature, it follows that though Entropy always increases, it becomes harder to increase the Entropy the more we increase it. Extending this argument to the Universe, is it correct to say that the Entropy of the Universe tends off to a maximum?
If so is it possible to calculate this maximum with respect to any reference? And what would the Universe be like when we reach this maximum?

[eoghan]

Yes... the Universe is going to reach a maximum of entropy, but guess when it will happen it's quite an impossible task. However it is known how the universe will look like at its maximum of entropy: it will be dead!
This death is called "Heat death" and you can refer to this http://en.wikipedia.org/wiki/Heat_death_of_the_universe (site) for more details

[Crazy Tosser]

I just hate thinking about heat death... It takes away hope...

[Mapes]

But we also know by the formula dS = d'Q/T that when we supply heat and increase the Entropy we also increase temperature. ... Extending this argument to the Universe, is it correct to say that the Entropy of the Universe tends off to a maximum?

It's difficult to extend this equation to the universe, since there isn't an external heat source. Instead, we should consider how entropy increases in a closed system. Spontaneous processes tend to smooth out gradients in mass, momentum, charge, temperature, and so on. At the inevitable point of maximum entropy, mass is evenly distributed throughout the cosmos and the temperature is uniform. But you are correct that we can only approach this point asymptotically, since the driving force to eliminate gradients is itself proportional to the magnitude of the unevenness.