Question

Compute the thermal efficiency for an ideal gas turbine cycle that operates with a pressure ratio of 6.75 and uses helium gas.

Answer 1

Given:

pressure ratio,
`r_(p)` = 6.75

Formula used:

`\eta = \frac{(r_(p))^{(\gamma -1)/(\gamma)}-1}{r_(p)^{(\gamma-1)/(\gamma)}}\\`

`\eta = 1- \frac{1}{r_(p)^{(\gamma-1)/(\gamma )}}` (1)

where,

`r_(p)` = pressure ratio

γ = specific heat ratio of a gas( here, helium gas it is 1.667)

Now,

Eqn (1 ) is for thermal efficiency of an ideal gas, using eqn (1), we get

`\eta = 1- \frac{1}{6.75^{(\ 1.667-1)/(\ 1.667 )}}`

\eta = 1- \frac{1}{2.1469} = 0.5342

percentage thermal efficiency, \eta =53.42%