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Brayton cycle working principle with P-v and T-s

Short answer

The Brayton cycle consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection. Air is compressed, heated in a combustor, expanded through a turbine, and exhausted. Net work output equals turbine work minus compressor work.

Explain the working principle of Brayton cycle with corresponding processes on P-v and T-s diagrams.

The Brayton cycle is the ideal air-standard cycle for gas turbines and jet engines. Air, the working fluid, is compressed, heated at constant pressure and expanded in a turbine. The turbine produces more work than the compressor takes, and the difference is the net output.

                 Fuel (Q_in)
                     |
                     v
          2   +-------------+   3
       +----->|  Combustor  |------+
       |      +-------------+      |
       |                           v
 [Compressor]=======shaft=======[Turbine]---> net work
       ^                           |
       | 1                       4 v
     Air in                     Exhaust

Processes

  1. 1-2: Isentropic compression in the compressor. Pressure and temperature rise; work is supplied.
  2. 2-3: Constant-pressure heat addition in the combustor (a heat exchanger in the ideal cycle). The temperature rises to the maximum, T₃.
  3. 3-4: Isentropic expansion in the turbine. Work is produced; part of it drives the compressor.
  4. 4-1: Constant-pressure heat rejection to the atmosphere (the hot exhaust cools to the inlet state).
 P-v diagram                      T-s diagram
 P                                T
 |  2 ____________ 3              |               3
 |   \             \              |              /|
 |    \             \             |             / |
 |     '.            '.           |           /   |
 |       '.            '.         |    2 _.-'     |
 |         '-._          '-._     |    |          4
 |             '- 1 _________ 4   |    |       .-'
 |                                |    |   _.-'
 |                                |    1.-'
 +----------------------> v       +--------------------> s
 1-2 isentropic compression       2-3 constant-P heat addition
 3-4 isentropic expansion         4-1 constant-P heat rejection

Key results

  • q_in = cp (T₃ − T₂), q_out = cp (T₄ − T₁)
  • w_net = q_in − q_out
  • η = 1 − 1/r_p^((γ−1)/γ), where r_p = P₂/P₁

A high pressure ratio gives high efficiency. The back-work ratio (compressor work/turbine work) is large, about 40-80 % for gas turbines.

✓ Answer checked by Claude Opus 5.5 (high effort)

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