UNIFIED ENGINEERING Fall 2005

Ian A. Waitz

Solution to T1 by Waitz. (Unified Thermodynamics)

It is understood at this point in Unified that you have only had one or two lectures on thermodynamics, and no propulsion and fluid mechanics lectures.  So what is expected is that you recognize conversions between various forms of energy when they occur and know the difference between transfers of energy called “work” and transfers of energy called “heat”.

• The process begins with a person converting chemical energy (glucose in the blood) to mechanical energy (moving body = changes in the body’s kinetic and potential energy), work (an energy transfer to the pump) and internal energy (increased body temperature). Due to the increased body temperature, some of this energy is transferred to the surroundings via heat transfer. This raises the internal energy of the surroundings. The efficiency of this process is about 20%. That is, of the chemical energy in the blood, about 20% is transferred to the pump; the rest goes to raise the internal energy of the body and the surroundings.
• The work done on (energy transferred to) the pump is used to draw in air, increase its internal energy, pressure and temperature, and push it in into the bottle. During the process some of the work is used to overcome friction. This along with the increased temperature of the compressed air leads to an increase in internal energy of the pump itself (it gets warm). Because of the increased pump temperature, some of this energy is transferred to the surroundings. This heat transfer raises the internal energy of the surroundings. I do not know the efficiency of a bicycle pump, but I expect that it is around 80%-90%.
• The air and water in the bottle are now at a higher pressure, temperature and internal energy. Depending on how long the person waits to launch the rocket, there may be some heat transfer to the surroundings—raising the temperature of the surroundings still further.
• When the rocket is launched, the air expands, pushing against (i.e., applying a force over a distance or doing work on) the propellant (the water). As the air expands, its internal energy is reduced. The work done by the air causes the propellant to move (i.e., gives the propellant kinetic energy). As the water passes through the exhaust nozzle it pushes on the walls of the nozzle doing work on the rocket. If the force on the rocket is greater than the weight of the rocket and the aerodynamic drag, the kinetic and potential energy of the rocket increase. The drag is caused by friction with the air molecules and pressure forces. The energy used to overcome the drag also ends up as increased internal energy (temperature ) in the surroundings.
• Once the water is exhausted, the trajectory of the rocket is set largely by a conversion of kinetic to potential energy although some energy is lost to the surroundings through drag.
• When the rocket hits the ground the kinetic energy is converted to internal energy in the bottle, the ground and the atmosphere.
• When the whole process is over, sitting on the ground are a bottle, some water, a person and a pump. All—the person, the pump, the bottle, the ground and the atmosphere—have seen a slight increase in internal energy (i.e. temperature) as a result of the whole process. In addition, the person has used a little bit of chemical energy.