This concept is quite different from what is commonly referred to as 'cold death.' 'Cold death' is when the universe continues to expand forever. Because of this expansion,the universe continues to cool down. Eventually, the universe will be too cold to support any life, it will end in a whimper. The opposite of 'cold death,' as you can see, is NOT 'heat death,' but actually the 'big crunch.' The 'big crunch' occurs when the universe has enough matter density to contract back on itself, eventually shrinking to a point. This shrinking will cause the temperature torise, resulting in a very hot end of the universe.
Discussions of the concept of 'heat death' can be found in some thermodynamics textbooks. The ideas of 'cold death' and the 'big crunch' can be found in textbooks on cosmology, such as The Early Universe by Kolb and Turner. Or, if you prefer and less technical discussion, you might want to try Black Holes and Time Warps by Kip Thorne.
The heatdeath of the universe will only occur if the universe will last for an infinite amount of time (i.e there will be no big crunch).
It will occur because according to the second law of thermodynamics, the amount of entropy in a system must always increase. The amount of entropy in a system is a measure of how disordered the system is - the higher the entropy, the more disordered it is..
It issometimes easier to imagine if you think of an experiment on earth. A chemical reaction will only occur if it results in an increase of entropy. Let us imagine burning petrol. We start of with a liquid that contains atoms arranged in long chains - fairly ordered. When we burn it, we create a lot of heat, as well as water vapour and carbon dioxide. Both of these are small gaseous molecules, so theamount of disorder of the atoms in their molecules has increased, and the temp. of the surroundings has also increased.
Now lets think what this means for the universe. Any reaction that takes place will either result in the products becoming less ordered, or heat being given off. This means at some time far in the future, when all the possible reactions have taken place, all that will be leftis heat (i.e electromagnetic radiation) and fundamental particles. No reactions will be possible, because the universe will have reached its maximum entropy. The only reactions that can take place will result in a decrease of entropy, which is not possible, so in effect the universe will have died.
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