Heat Engine - Is it possible to reroute lost energy to the engine again? Recently, I have studied thermodynamics in my physics class and have gone over the topic of the heat engine and how it works. In my understanding, some of the energy is used for work (to move the car in the case of a car engine) and the rest is lost to the surroundings through the exhaust. My question is, is it possible to reroute the lost energy or collect it back into the engine again to use that energy for work? If it would increase the heat of the engine too much, isn't it possible then to move it around the car to avoid overheating the engine? Is it possible to do any of what I'm proposing to increase efficiency, and if possible, has it already been attempted?
Thank you for your time.
 A: In a heat engine the work is done by moving heat from a high temperature region to a low temperature region.  Once the exhaust is at a lower temperature, there's no way to feed it back into the high temperature region to generate more power.  You'd just decrease the higher temperature, making the engine less efficient.
We do, however, try to regain work when we can.  Modern power stations are often multi-stage devices.  Rather than just having one transition from a high pressure to a low pressure, we often have several stages, the exhaust of each stage feeds into the inlet of the next stage.  We do this because this lets us tune the different parts of the turbine to better extract power.
Turbochargers are another interesting example.  In a turbocharger, we use the energy in the exhaust to spin a compressor that compresses the air going into the engine.  This isn't quite the same as what you are taking about, but is an example of us getting as much energy out of the combustion in an engine as possible.
A very extreme example would be a Dyson sphere.  A Dyson sphere is a fictional superstructure the size of our entire orbit.  The idea of the Dyson sphere is to collect all of the energy from a star.  One of the popular constructions people have drempt up along these lines is the Matrioshka brain.  In this construction, one has many layers of heat engines, each generating power using the difference in temperature between the layer outside of it and the layer inside of it.
