Problem
Climate change represents a global threat to the prosperity and security of humans and other species. An added element of uncertainty regarding Earth's climate future has to do with feedback loops in the climate system.
One positive feedback is associated with the loss of glaciers, sea ice, and snow pack. Ice reflects about 90% of the radiant energy incident upon it, so the polar ice caps reflect significant amounts of solar energy. As the planet warms and surface ice is lost, the Earth becomes less reflective, absorbs more energy from the sun and thus heats up more rapidly.
A negative climate feedback is associated with the amount of energy that Earth loses to space. As the planet warms the Stefan-Boltzmann law indicates that it will radiate more energy.
Earth's average surface temperature over the 20th century was 56.7F. Since 1880 the average temperature of Earth has increased by about .830 degrees C.
1. What is the fractional increase in power radiated away by the planet in 2021 relative to 1880?
2. Assume that the emissivity of Earth is constant.