An air-powered car is powered using high pressure compressed air stored in a tank. The pressurized tank is connected to an air-powered engine. The volume of the tank is 0.3 m3, and the initial temperature and pressure of air inside the tank is 20°C and 30 MPa, respectively. Using online resources, analyze the efficiency of the Air Car.
Using thermodynamics we can estimate the efficiency of the air car, as follows:
The efficiency of the air car is equal to 100×(output energy)/(input energy). The input energy is equal to the amount of energy required to fill the tank with compressed air. Let's assume an ideal isothermal (constant temperature) process where the pressurized air being pumped into the tank is kept as close as possible to the ambient air temperature. This minimizes the pumping energy required to pump the air into the tank. This is achieved by cooling the pressurized air before it enters the tank. If the air is not simultaneously cooled as it is pumped into the tank it will reach a very high temperature, which will require a greater pumping energy than cooler air. Air heating up due to compression is a fundamental property of gases (which can be modeled here as an ideal gas, where PV = mRT). If you compress air into a smaller volume, it will tend to heat up.
It is important to mention, however, that (in the absence of air cooling) the extra input (pumping) energy would result in extra output energy as you drive the car, but only if the heated air in the tank could maintain its temperature. But in reality, the heated air would cool down to the ambient temperature. And that extra pumping energy would be for nothing (i.e. it wouldn't be recovered in the driving phase). So this is one reason why we have to cool the air as close as possible (within practical limits) to ambient temperature, as it enters the tank. This is achieved with multi-stage cooling.
With isothermal pumping of the air into the tank, the (ideal) input energy is, Ein = P1V1ln(P2/P1), where P1 and V1 is the initial (atmospheric) pressure and initial volume of the air, respectively, and P2 is the pressure of the air after it's pumped into the tank. From the ideal gas equation given above, and given an isothermal process, P1V1 = P2V2, where V2 is the volume of the tank. We can then calculate V1 = 90 m3.
Substituting P1 = 0.1 MPa (atmospheric pressure), P2 = 30 MPa, and V1 = 90 m3 into the equation above we calculate Ein = 51.3 MJ (megajoules).
Now, in reality the air heats up somewhat between cooling stages so this "forces" the compressor to use more than 51.3 MJ to pump air into the tank. Based on data from the European Fuel Cell Forum, a realistic efficiency factor for multi-stage cooling is 48% (ref: http://www.efcf.com/reports/E14.pdf). So the actual input energy is Ein = 51.3/0.48 = 107 MJ.
Once in the tank, the air will cool until its temperature reaches the ambient outdoor temperature. The energy of the air at this point will be 51.3 MJ.
Note that 51.3 MJ is greater than the actual energy that will be extracted from the tank to power the car. This is due to thermodynamic (physical) losses (a form of thermodynamic irreversibility). To keep these losses as low as possible it is necessary that the air is heated up as it expands inside the engine, after exiting the tank. Since air has a tendency to cool down upon expanding it is best to keep its temperature as high as possible using the ambient air as a heating source. In other words, we wish to maintain the (expanding) air temperature as close as possible to its temperature inside the tank. If this could be accomplished perfectly then the extracted energy will exactly equal 51.3 MJ. But in reality this is not the case. The air will unavoidably cool, so to help counteract this, multi-stage heating is used to heat the expanding air as it exits the tank and goes into the engine.
Based on data from the European Fuel Cell Forum, a realistic efficiency factor for multi-stage heating is 84% (ref: http://www.efcf.com/reports/E14.pdf). So the actual output energy is Eout = 51.3×0.84 = 43 MJ.
Therefore, the thermodynamic efficiency of the Air Car is 100×(Eout/Ein) = 40%.
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