Superheated steam at 500 degree C and 30 bar is expanded in

Superheated steam at 500 degree C and 30 bar is expanded in an adiabatic turbine to 10 bar and the product is all saturated vapor. If the feed of steam is 15 kg/s of superheated steam, what is the power output of the turbine?

Solution

Given at the inlet of steam, P = 30 bar, T = 500^oC

mass flow rate of steam, m = 15 kg/s

From the steam tables, we have at P = 30 bar and T = 500^oC,

Specific enthalpy, h₁ = 3457.040 KJ/kg

Specific entropy, s₁ = 7.236 kJ/kgK

Since the expansion process over the turbine is adiabatic, hence at the outlet of steam turbine,

Specific entropy, s₂ = s₁ = 7.236 kJ/kgK

Given that at the exit of the turbine, we have saturated vapor. From steam tables, for s = 7.236 kJ/kgK and saturated vapor conditions, we have, pressure

P₂ = 1.45 bar

Specific enthalpy of saturated vapor at this pressure, h₂ = 2691.577 kJ/kg

Power Output of the turbine, as per steady flow energy equation (neglecting the kinetic and potential energy terms and treating the process to be reversible)

W = m(h₁ - h₂)

= 15 X (3457.040 -  2691.577)

= 11481.945 kW

W = 114.82 MW