Steam at 175 [C] and 300 kPa flows into a steam turbine at rate of 5.0 kg/sec. Saturated mixture of liquid and steam at 100 kPa flows out at the same rate. The heat loss from the turbine is 1,500 kW. Assuming that 60% of the steam is condensed into liquid at the outlet, how much shaft work can the turbine produce?

The amount of shaft work the turbine cam do per second is 3660.29 kJ

Explanation:

The given parameters are;

Pressure at entry p₁ = 300 kPa

The mass flow rate,   = 5.0 kg/sec

The initial temperature, T₁ = 175°C

Therefore;

The enthalpy at 300 kPa and 175°C, h₁ = 2,804 kJ/kg

At the turbine exit, we have;

The pressure at exit, p₂ = 100 kPa

The quality of the steam at exit, in percentage, x₂ = 60%

Therefore, for the enthalpy, h₂ for saturated steam at 100 kPa and quality 60%, we have;

h₂ = 417.436 + 0.6 × 2257.51 = 1771.942 kJ/kg

Heat loss from the turbine, = 1,500 kW

By energy conservation principle we have;

dE/dt = - + ∑+ +) - ∑ + + )

0 = -  -   + -  

= × (h₁ - h₂) - = 5.0×(2,804 - 1771.942) - 1500 = 3660.29 kJ/s

The rate of work of the shaft = 3660.29 kJ/s

The amount of shaft work the turbine cam do per second = 3660.29 kJ.