When will the earth be destroyed?
in about 5 billion years
Destruction is closer than you think... the Earth without life is simply not Earth.
http://en.wikipedia.org/wiki/Future_of_the_Earth
During the next four billion years, the luminosity of the Sun will steadily increase, resulting in a rise in the solar radiation reaching the Earth. This will cause a higher rate of weathering of silicate minerals, which will cause a decrease in the level of carbon dioxide in the atmosphere. In about 600 million years, the level of CO2 will fall below the level needed to sustain C3 carbon fixation photosynthesis used by trees. Some plants use the C4 carbon fixation method, allowing them to persist at CO2 concentrations as low as 10 parts per million. However, the long-term trend is for plant life to die off altogether. The die off of plants will be the demise of almost all animal life, since plants are the base of the food chain on Earth.
Its still earth even with no life. You assume that absolutely no life will survive tho. What about extremaphobes? To quote a man that turned into a giant fly and survived run away dinosaurs,
The change will be so slow that life will evolve to compensate. I believe there will be life on earth right up until the end. We may not recognize it but it will be there none the less.