Kelvin Cooling Time

Presuming that the Earth was once very hot and had cooled to about 300K by radiation into space, Kelvin calculated a radiative cooling time for the Earth. The cooling time can be modeled by

假定地球曾经非常热，并通过辐射到空间冷却至约300K，开尔文计算了地球的辐射冷却时间。该冷却时间可以建模为

It is reasonable to assume that the term involving the early hot temperature of the Earth can be neglected. If the hot temperature is more than 3.16 times the final temperature, then the contribution of the high temperature term is less than 1%. For example, for the 300K ambient on the earth, an original temperature higher than 1000K would make the second temperature in the expression above negligible. Taking only the term involving the current Earth temperature, the cooling time can be estimated as follows:

合理地假设地球早期高温项可以被忽略。如果高温是最终温度的3.16倍以上，那么高温项的贡献将小于1%。例如，对于地球上的300K环境温度，如果初始温度高于1000K，那么上述表达式中的第二个温度项将可以忽略不计。仅考虑当前地球温度项，冷却时间可以估计如下：

The Kelvin cooling time for the Earth is then about 30,000 years. There are many ways you could refine the calculation above, but the point is made that this cooling time is much shorter than the age of the Earth as determined by other means.

地球的冷却时间约为30,000年。你可以用多种方法改进上述计算，但要点在于这个冷却时间远短于通过其他方法确定的地球年龄。

Kelvin's calculation pointed to the the existence of an internal heat supply which has kept the Earth hot long after the radiative cooling time. His work was done before the discovery of radioactivity and the understanding that natural radioactive decay provides a source of heat to the Earth.

开尔文的计算指出，存在一种内部的热源，使地球在放射冷却时间之后仍保持炽热。他的工作是在放射性发现以及认识到自然放射性衰变能为地球提供热源之前完成的。

Kelvin Cooling Time for the Earth