 http://session.masteringphysics.com/problemAsset/1013832/78/1013832.jpg |
In the Doctor
Who episode The Long Game, an alien entity is
discovered to be emitting tons and tons of heat,
enough to heat up the entire space station (which we
should mention housed about a thousand people). The
room in which the alien is contained, interestingly
enough, is covered with frost. What the episode is
saying is happening is that the alien Jagrafess has a
metabolism that creates a ton of heat, and in order to
maintain the room where he's kept they have to pump
all of the heat out and with that heat the entire
space station is heated up. The heat engine they
supposedly create to keep the Jagrafess from
overheating is not possible, but the idea of freezing
a room with a massive hot sweaty alien is pretty cool.
As a thought experiment, we are going to look at the
human metabolism and see how much heat it produces and
hope to discover how many people it would take to
produce that much heat. |
| We will assume that the space station in the episode is 167 times the size of the International Space Station that usually houses 6 people. The amount of inhabitable space inside of the space station would have to be about 64,667 meters cubed to accommodate that many people. To heat that amount of space just one degree centigrade would require approximately 82,476 kilojoules. The heat produced by the average male metabolism doing moderate work is 160 Watts or 160 Joules per second. It would take a single person about 6 days to heat up the entire space station one degree, or a thousand people would take 8.56 minutes to heat the entire volume of the station one degree Celsius. Because there is very little heat loss in the vacuum of space, the heat of this creature and the people would be immense and continuous. With nowhere for this heat to go (unless they had an opening to release heat) they would probably all die. For the top chamber of the space station to be a freezer, it would require enough energy to cancel out the Jagrafess' heat and then drop the temperature another 20 or so degrees Celsius. Needless to say, that would be a huge amount of power. |  http://img2.wikia.nocookie.net/__cb20101212192101/tardis/images/1/15/Jagrafess.jpg |
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