People have dreamed of constructing a machine that would run forever. Thermodynamics tells that there are intrinsic limitations to the efficiency of any process that derives work from heat. This limitation is known as the thermodyanmic efficiency. The reason for this limitation is that any real heat engine must operate at a working temperature, at which a hot gas expands to do useful work and an exhaust temperature, at which heat is expelled into the environment. The only way to reach 100% efficiency is for the exhaust temperature to reach 0 Kelvin. This is not very realistic and it is, in fact, technically impossible. Although we can get very close to 0 Kelvin we cannot actually reach zero. The energy cost for getting close to absolute zero is very high and so it is not feasible to run an engine at such a low temperature. In practice, it is not practical to run an engine with an exhaust temperature below the ambient temperature. While one may use clever ideas (such as using underground shafts) to reduce the ambient temperature, there are clear limitations. On the high temperature side there are obvious limitations due to the melting point of metals. Long before one reaches the melting point the stress on an engine would be very great and would lead to a reduction in useful life if the operating temperature were too high. We consider the derivation of a formula that shows the intrinsic limitations to thermodynamic efficiency in the following video.
