For the next week "we" will look at one of the most fundamental questions about a star:
How does a star produce all the energy that it radiates away into space?
The answer to this explains the existence of the main sequence in the HR Diagram and leads into the next big topic  the formation and evolution of stars.
So, a 3000 gram bucket of coal is good for about 1.2 x 10^{16} ergs or 300 Kilowatthours. This would run a little space heater for about an hour.
Now, the Sun's mass is 2 x 10^{33} grams. If the sun was made of
coal and producing energy via conventional combustion, it could generate a
total energy of:
Lifetime is calculated by taking the total energy available divided by the rate
at which you are using up the energy. The sun uses up energy at a rate of
1 L_{} = 4 x 10^{33} ergs/sec.
Lifetime  =  8 x 10^{45} ergs x  1 sec 

4 x 10^{33} ergs  
=  2 x 10^{12} secs x  1 min 
x  1 hr 
x  1 day 
x  1 year 

60 sec  60 min  24 hr  365 days  
=  6300 years 
Anytime you have a collection of mass (for example a gas of atoms and molecules), it has an associated Gravitational Potential Energy  GPE. For a big ball of gas, the GPE goes like:
GPE =   3 
x  M^{2} 
x  G 
5  R 
where R is the radius of the ball of gas, M is the total mass, and G is the "gravitational constant".
Similarly, because the Earth exerts a gravitational pull on objects at its
surface and in space, these objects all have an associated GPE.
How much total GPE does the Sun have that could be turned into radiation as the Sun shrinks?
GPE =  3 
x  M_{}^{2} 
x  G  ~ 2 x 10^{48} ergs 
5  R_{} 
This shows that converting GPE is a pretty efficient process compared to chemical burning:
2 x 10^{48} ergs 
= 10^{15} ergs/gram 
2 x 10^{33} grams 
This is about 250 times more efficient than chemical burning.
Lifetime = 2 x 10^{48} ergs x  1 sec 
= 5 x 10^{14} sec 
4 x 10^{33} ergs 
This converts to 16 million years  still too short!
The Earth is around 4 billion years old (plus the Sun would have been much
bigger in the past).