Air-Standard Cycle

Pasted image 20240108141004.png

Pasted image 20240108141029.png

Pressure ratio: $r = \frac{P_{2}}{P_{1}}$

	Temperature	Specific Volume
$1 \to 2$	$T_{2} = T_{1} r^{\frac{γ - 1}{γ}}$	$v_{2} = v_{1} r^{- \frac{1}{γ}}$
$3 \to 4$	$T_{4} = T_{3} r^{\frac{γ - 1}{γ}}$	$v_{4} = v_{3} r^{- \frac{1}{γ}}$

	Specific Work
Compressor	$w_{c o m p} = C_{p} T_{1} [1 - r^{\frac{γ - 1}{γ}}]$
Expander	$w_{e x p} = C_{p} T_{3} [1 - r^{\frac{γ - 1}{γ}}]$
Net	$w_{n e t} = C_{P} T_{1} [(1 - r^{\frac{γ - 1}{γ}}) + \frac{T_{3}}{T_{1}} (1 - r^{\frac{γ - 1}{γ}})]$

	Specific Heat
Intake	$q_{i n} = C_{P} T_{1} [1 - \frac{T_{3}}{T_{1}} r^{\frac{γ - 1}{γ}}]$
Exhaust	$q_{o u t} = C_{P} T_{1} [\frac{T_{3}}{T_{1}} - r^{\frac{γ - 1}{γ}}]$

Coefficient of Performance:

In laymans terms, $β = \frac{what we want}{what we give}$ . This is not an Efficiency!

β = \frac{q_{i n}}{| w_{n e t} |} = \frac{1}{r^{\frac{γ - 1}{γ}} - 1}