# Residence time of energy in Earth's atmosphere and in the Sun

## TL;DR

This paper extends the concept of residence time from matter to energy, estimating the average energy residence time in Earth's atmosphere and the Sun, providing insights into their energy dynamics.

## Contribution

It introduces a novel application of residence time to energy and estimates these timescales for Earth and the Sun, aligning with known astrophysical scales.

## Key findings

- Energy residence time in Earth's atmosphere is about 56 days.
- Energy residence time in the Sun is approximately 26 million years.
- Results align with the Kelvin-Helmholtz time scale.

## Abstract

In atmospheric chemistry, a parameter called residence time can be defined for each gas as T=M/F, where M represents the average mass in the atmosphere and F is the total average influx or outflux, which in time averages are equal. In this paper we extend this concept from matter to energy which is also a conservative quantity and estimate the average residence time of energy in Earth's atmosphere and in the Sun. For our atmosphere, the estimation amounts about 56 days and for the Sun the residence time is about 2.6 x 10^7 yr, which agrees with the Kelvin-Helmholtz time scale.