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

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%