Net Work of an Open Carnot Cycle

Ch 9, Lesson A, Page 4 - Net Work of an Open Carnot Cycle

• The total shaft work for a Carnot Cycle is the sum of shaft work for each step in the cycle.
• When the cycle is an internally reversible, SISO cycle operating at steady-state, we can use the equation for Ws-dot over m-dot from page 2 for each process in the cycle.
• Because the shaft work is positive when pressure decreases and negative when pressure increases, the net shaft work for the cycle is equal to the area enclosed by the process path.
• Notice that this process moves clockwise around the process path. V-hat is always larger when P is decreasing, along the path 1-2-3, than it is when P is increasing along the path 3-4-1.
• Therefore the net shaft work for the cycle is positive and this is a power cycle.
• What if states 1, 2, 3, and 4 are the same states that the closed system, from the previous page, passed through in that cycle.
• Well, then the enclosed areas would be the SAME.
• We can conclude that Ws-dot over m-dot for an open system is the same as Wb over m for a closed system when the two processes follow the same path.
• That is very cool, but it can be confusing.  This does NOT mean that boundary work shaft work are the same thing or that they are always equal.
• They are not the same and they are only equal for these very special open and closed systems that also follow the exact same process path.
• That is the end of our whirlwind review of work and PV Diagrams for thermodynamic cycles.
• Next we will take a look at TS Diagrams and the relationship between heat and areas on these diagrams.