Question

How many Joules of energy are required to run a 100W light bulb for one day?
Burning coal yields about 30 x 10^6 J of energy per kilogram of coal burned. Assuming that the coal power plant is 30% efficient, how much coal has to be burned to light that light bulb for one day?

Answer 1

a) Power (P) is work (W) per time (t) otherwise know as rate of work, so solve:\[P=\frac{ W }{ s } \rightarrow W=Pt=100W1day \frac{ 24h }{ 1day }\frac{ 3600s }{ 1h }=8640000J\]
b) This one is harder. So you now the work you must do from the answer you got on a). Now you know that for every kilogram of coal you burn you get 30% of 30x 10^6 J of work (w) done. So to figure out how much coal (m) you need you must solve this equation:\[W=\frac{ 30 }{ 100 }wm \rightarrow m=\frac{ 100W }{ 30w }=\frac{ 100 \times 8640000J }{ 30 \times 30 \times 10^{6}\frac{ J }{ kg } }=0.96kg\]