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Consider a simple gas turbine (Brayton) cycle and a gas turbine cycle with perfect regeneration. In both the cycles, the pressure ratio is 6 and the ratio of the specific heats of the working medium is 1.4. The ratio of minimum to maximum temperatures is 0.3 (with temperatures expressed in K) in the regenerative cycle. The ratio of the thermal efficiency of the simple cycle to that of the regenerative cycle is._____.
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- 4.5453
- 3.4557
- 2
- 0.8021
Correct Option: D
Brayton cycle
| ηBrayton = 1 – | |
| (rρ)γ-1/γ |
given rρ = 6, γ = 1.4
| ∴ ηBrayton = 1 – | = 0.4006 | |
| (6)1.4-1/1.4 |
| effectiveness ε = | = 1 | |
| Cρ(T3 - T2) |
T3 = T5
| Given | = 0.3 = | ||
| Tmax | T4 |
Wnet = WT – WC
= Cρ (T4 – T5) – Cρ (T2 – T1)
= Cρ (T4 – T3) – Cρ (T2 – T2 )[∵ T4 = T3]
| ηRegenerative = | |
| Heat-supplied |
| = | |
| Cρ(T4 – T3) |
| = 1 - |  |  | |
| T4 - T3 |
| = | 1 - T1 | | - 1 | | |
| T1 | |||||
| 1 - T4 | | 1 - | | ||
| T4 | |||||
| ηRegenerative = 1 - | | - 1 | | |||
| T1 | ||||||
| T4 | 1 - | |||||
| T4 | ||||||
| ηRegenerative = 1 - | | - 1 | | ||
| T4 | 1 - | ||||
| r(ρ)γ-1/γ | |||||
| = 1 - | r(ρ)γ-1/γ | |
| T4 |
= 1 - 0.3(6)1.4-1/1.4 = 0.4994
| = | = 0.8021 | |||
| ηRegenerative | 0.4994 |
