Question

. A steam turbine operates between 500°C and 3.5 MPa to 200°C and 0.3 MPa. If the turbine generates 750 kW and the heat loss is 100 kW, what is the flow rate of steam through the turbine?

Answer 1

1.757 kg/s

Step-by-step explanation:

According to the First Law of Thermodynamics, the physical model for a turbine working at steady state is:

`-\dot Q_(out) - \dot W_(out) + \dot m \cdot (h_(in)-h_(out))=0`

The flow rate of steam is:

`\dot m = (\dot Q_(out)+\dot W_(out))/(h_(in)-h_(out))`

Water enters and exits as superheated steam. After looking for useful data in a property table for superheated steam, specific enthalpies at inlet and outlet are presented below:

`h_(in) = 3451.7 (kJ)/(kg) \\h_(out) = 2967.9 (kJ)/(kg) \\`

Finally, the flow rate is calculated:

`\dot m = (100 kW + 750 kW)/(3451.7 (kJ)/(kg) - 2967.9 (kJ)/(kg))\\\dot m =1.757 (kg)/(s)`