The compression ratio of a gas power plant cycle corresponding

The compression ratio of a gas power plant cycle corresponding to maximum work output for the given temperature limits of T_min and T_max will be

W = Turbine work – compressor work
W = C_p [(T₃ – T₄) – (T₂ – T₁)]

Let	T₃	= t and	T₂	=	T₃	= C
	T₁		T₄		T₄

W = C_pT₁		t		1 –	1		- (C - 1)
					C

For maximum work output

dW	= C_pT₁		T			1		- 1		= 0
dc						C²

gives C² = √t