Final answer:
The atmosphere's height would decrease as density increases if it maintained uniform density throughout because Earth's gravity would compress a denser atmosphere more, causing it to not extend as far into space.
Step-by-step explanation:
The question asks how high the atmosphere would extend if it were of uniform density throughout. The correct answer to this question is that the height of the atmosphere would decrease as the density increases. This concept is based on the understanding that Earth's gravity influences the atmosphere's height. If the density were uniform, the gravitational pull would cause a thicker, denser atmosphere to be more compressed and thus not extend as far into space. In reality, the density of our atmosphere decreases with altitude due to the change in gravitational pull and other factors like temperature and the presence of varying gases at different layers.
The fact that air density decreases with altitude under normal circumstances is demonstrated by an exponential decrease in air density with altitude for a column of air at constant temperature. However, if we assume a uniform density, the height at which the atmosphere would extend depends on the density and the Earth's gravity. A denser atmosphere would mean more mass is contained within a smaller volume, which would not extend as high because of the gravitational pull.