Consequently, the work done on the atmosphere is
The net work is now
Wnet = 1RT1 - iRTs + W23 = |R(T1 - Ts)+ ICv (T1 - Ts)
Still for the example being considered, the specific net energy is 4.2 MJ/kmole or 150kj/kg. Compare with the 5.7 MJ/kmole or 204kJ/kg for the isothermic case and with the 47,000 kJ/kg for the typical gasoline.
Clearly, the specific energy of the cryogen will increase with increasing operating pressure. The gain, however, is logarithmic. Thus, by raising the pressure to 10MPa (a factor of 10), the specific energy rises to 11.4 MJ/kmole, a gain of 2. Observe that 10MPa correspond to approximately 100 atmospheres and would lead to a rather heavy (and expensive) engine.
Gasoline has to be used in an internal combustion engine with some 20% efficiency, while the pneumatic motor used in the cryogenic engine can have a very high component efficiency. This would reduce the practical specific energy advantage of gasoline to a factor of 40 over the nitrogen.
In practice, the Ordonez engine has yielded around 19 kJ/kg thus far. A demonstration car using the engine does 0.3 mile to the gallon, which is not practical. The efficiency will probably be improved.
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The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.