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Global Warming

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

According to wikipedia, the atmosphere has a mass of $5\times10^{18}kg$, and the specific heat capacity of air is about $1\mathrm{Jg^{-1}K^{-1}}$. Therefore, the amount of energy needed to raise the average temperature of the atmosphere by $0.4^{\circ}\mathrm{C}$ is
$$1\times10^3\mathrm{Jkg^{-1}K^{-1}}\times0.4\mathrm{K}\times5\times10^{18}\mathrm{kg} = 2\times10^{21}\mathrm{J}.$$


Coal has an energy density of 24 megajoules per kilogram. Assuming 100% of the energy released from burning heats the atmosphere, we'll need $\frac{2\times10^{21}\mathrm{J}}{ 24\times10^6\mathrm{Jkg^{-1}}} = 8\times10^{13}\mathrm{kg}$. Assuming a global population of 6 billion this corresponds to $\frac{8\times10^{13}}{6\times10^9\times30\times52} = 9$ kilograms per person per week per year for the last 30 years. 


This is probably a significant underestimate of the amount of fuel used, as not all the energy released from burning goes straight to the atmosphere. Also, this calculation ignores the fact that different fuels have different energy densities. 

The greenhouse effect is also responsible for some of the temperature increase.