UNIFIED ENGINEERING Fall 2004

Ian A. Waitz

Problem T9 (Unified Thermodynamics)

Consider a Brayton cycle for an ideal gas. Assume all processes are quasi-static.

1. Derive expressions for the shaft work, flow work, work, and heat transfer for each leg of the cycle in terms of the temperatures T₁, T₂, T₃, T₄, c_v, c_p, and R.
2. Using these expressions, show that the net work for the cycle is equal to the net heat for the cycle.
3. Show that the net flow work for the cycle is zero and that the net shaft work is equal to the net work for the cycle.
4. Describe in a sentence or two what flow work is.
5. For the ABB gas turbine (problem T7) calculate the work, shaft work, and flow work for the turbine. What fraction of the shaft work is used to drive the compressor?