A Brayton cycle has air into the compressor at 95 kPa, 290 K, and has an efficiency of 50%. The exhaust temperature is 675 K. Find the pressure ratio and the specific heat addition by the combustion for this cycle. (Borgnakke, 02/2019, p. P-93) Borgnakke, C., Sonntag, R. E. (02/2019). Fundamentals of Thermodynamics, Enhanced eText, 10th Edition [VitalSource Bookshelf version]. Retrieved from vbk://9781119494966 Always check citation for accuracy before use.

The specific heat addition is 773.1 kJ/kg

Explanation:

from table A. 5 we get the properties of air:

k=specific heat ratio=1.4

cp=specific heat at constant pressure=1.004 kJ/kg*K

We calculate the pressure range of the Brayton cycle, as follows

n=1 - (1 / (P2/P1) ^ (k-1) / k))

where n=thermal efficiency=0.5. Clearing P2/P1 and replacing values:

P2/P1 = (1/0.5) ^ (1.4/0.4) = 11.31

the temperature of the air at state 2 is equal to:

P2/P1 = (T2/T1) ^ (k/k-1)

where T1 is the temperature of the air enters the compressor. Clearing T2

11.31 = (T2/290) ^ (1.4 / (1.4-1))

T2=580K

The temperature of the air at state 3 is equal to:

P2/P1 = (T3/T4) ^ (k / (k-1))

11.31 = (T3/675) ^ (1.4 / (1.4-1))

T3=1350K

The specific heat addition is equal to:

q=Cp * (T3-T2) = 1.004 * (1350-580) = 773.1 kJ/kg