Problem $1(5$ Points$-$ show all work$)$

The United States has about $300$G W of coal$-$fired power plants that in total emit about $2$ Gt of CO$2/$yr while generating about $2$ million GWh$/$yr of electricity.

$($a$)$ What is their overall capacity factor?

$($b$)$ What would be the total carbon emissions $($Gt CO$2/$yr$)$ that could result if all of the coal plants were replaced with $50\%-$efficient NGCC plants that emit $13\mathrm{.}7$ kg CIGJ of fuel?

$($c$)$ Total US CO$2$ emissions from all electric power plants is about $5\mathrm{.}8$ Gt$/$yr$.$ What percent reduction would result from switching all the above coal plants to NGCC$?$