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TEA [102]
3 years ago
12

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

Engineering
1 answer:
pychu [463]3 years ago
4 0

Solution:

Given:

pressure ratio, r_{p} = 6.75

Formula used:

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

\eta = 1- \frac{1}{r_{p}^{\frac{\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^{\frac{\ 1.667-1}{\ 1.667 }}}

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

percentage thermal efficiency, \eta =53.42%

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