Question

Air enters the compressor of a gas turbine at 1 bar, 30°C and leaves the compressor at 4 bar. The compressor has an efficiency of 82%. Calculate per kg of air

(a) The work of compression

(b) The reversible work of compression

(c) The irreversibility. For air, use \(\frac{T_{2s}}{T_1} = \left(\frac{p_2}{p_1}\right)^{\gamma-1/\gamma}\)

Where T_2s is the temperature of air after isentropic compression and γ = 1.4. The compressor efficiency is defined as (T_2s – T₁) / (T₂ – T₁), where T₂ is the actual temperature of air after compression.

Answer 1

(b) Minimum work required for compression is isentropic work

(a) Actual work = \(\frac{147.92}{0.82}\) = 180.4 kJ/kg

∴ Extra work 32.47 kJ will heat the gas from T'₂ to T₂

(c) Irreversibility (I) = (180.4 – 147.92) kJ/kg

= 32.48 kJ/kg