Question

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?

Answer 1

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

Step-by-step explanation:

The given parameters are;

Pressure at entry p₁ = 300 kPa

The mass flow rate,
`\dot {m}` = 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,
`h_l`= 1,500 kW

By energy conservation principle we have;

dE/dt =
`\dot Q` -
`\dot W` + ∑
`m_i \cdot (h_i`+
`ke_i` +
`pe_i`) - ∑
`m_e \cdot (h_e` +
`ke_e` +
`pe_e` )

0 = -
`h_l` -
`\dot W` +
`m_i \cdot h_i` -
`m_e \cdot h_e`

`\dot W` =
`\dot {m}` × (h₁ - h₂) -
`h_l` = 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.