Calculate the thermal efficiency (ηth) for the actual cycle using pump efficiency (ηpump) = 0.85. You’ll need to find the high-pressure turbine isentropic efficiency assuming the measured highpressure turbine exit temperature (Tactual) and pressure, 300 ℃ and 1.8 MPa respectively. Assume a value for (ηTurbine) if you have trouble with the calculation or don’t trust the result of your calculation

The thermal efficiency (η) for the actual cycle is 27.567 %.

Explanation:

From thermodynamic super heated steam tables, we have

At 8 MPa and 500 °C

h₁ = 3399.37 kJ·kg⁻¹

s₁ = 6.7264 kJ·kg⁻¹·K⁻¹

With  measured high- pressure turbine exit temperature of 300 °C (T) and pressure of 1.8 MPa we have

From the super heated steam tables at T = 300 °C and P = 1.8 MPa, we have

h₂ = 3029.74 kJ·kg⁻¹

s₂ = 6.83974 kJ·kg⁻¹·K⁻¹

From the super heated steam tables at 1.8 MPa and 500 °C, we have

s₃ = 7.4996 kJ·kg⁻¹·K⁻¹ and h₃ = 3470.272 kJ·kg⁻¹

s₃ = s₄ = 3470.272 kJ·kg⁻¹ from which we have the dryness fraction as 0.89515 through the following equation

Where:

= 1.1694 kJ·kg⁻¹·K⁻¹

= 6.3345 kJ·kg⁻¹·K⁻¹

at 1 MPa = 762.283 kJ·kg⁻¹

Work done by pump = = 0.00114118 m³·kg⁻¹ × ( 8 MPa - 1 MPa)

= 798826 J/kg

Where the pump efficiency = 85 % we have

Work done by pump = 0.85 × 798826 J/kg = 679002.1 J/kg

Also work done by pump = h₆ - h₅ = 679002.1 J/kg = 679.0021 kJ/kg

Therefore h₆ = h₅ + 679.0021 kJ/kg = 762.283 kJ·kg⁻¹·K⁻¹ + 679.0021 kJ/kg

= 1441.2851 kJ/kg

Thermal efficiency is given by

= = = 0.2757 or 27.567 %

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