Global warming

6453 /www/nrich/html/content/id/6453/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/7418">Warm-up</a></li> <li><a href="http://nrich.maths.org/7428">Try this next</a></li> <li><a href="http://nrich.maths.org/6456">Think higher</a></li> <li><a href="http://plus.maths.org/content/maths-and-climate-change-melting-arctic">Read: mathematics</a></li> <li><a href="http://en.wikipedia.org/wiki/Global_warming">Read: science</a></li> <li><a href="http://motivate.maths.org/content/node/103">Explore further</a></li> </ul> <div> </div> In this investigation you will need to use a variety of pieces of physical data to come up with a reasonable estimate. What data will you need? Where will you find it? What estimates are sensible? What modelling assumptions are you making at each step? These are the sorts of questions that you will need to ask yourself as you undertake your investigation . As a conservative estimate, the average temperature of the atmosphere has increased by $0.4^\circ\mathrm{C}$ over the last thirty years. Estimate how much energy has gone into warming up the planet in this way. Estimate how much burned fuel would be needed to give rise to this increase on the assumption that this were the only cause of changes in the earths temperature. How much fuel burned per week over the last thirty years per person on the planet would this correspond to? What do you think about your answer? How does the amount of burned fuel correspond to the levels of fuel actually used? What other factors would come into a more sophisticated analysis of global warming? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> It is not envisaged that <a href="http://nrich.maths.org/6453">this problem</a> would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> According to <a href="http://en.wikipedia.org/wiki/Atmosphere_of_Earth">wikipedia</a>, the atmosphere has a mass of $5\times10^{18}kg$, and the <a href="http://en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities">specific heat capacity of air</a> 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 <a href="http://en.wikipedia.org/wiki/Energy_density#Common_Energy_Densities">24 megajoules</a> 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 <a href="http://en.wikipedia.org/wiki/Greenhouse_effect">greenhouse effect</a> is also responsible for some of the temperature increase. </mdoxml> 2 4 0 0 0 1 0 Global warming How much energy has gone into warming the planet? Applications Maths Supporting SET Using, Applying and Reasoning about Mathematics Investigations Applications STEM - physical world