Answer:
, ![\dot H_{out} = 39632.62 kW](https://tex.z-dn.net/?f=%5Cdot%20H_%7Bout%7D%20%3D%2039632.62%20kW)
Explanation:
Since there is no information related to volume flow to and from turbine, let is assume that volume flow at inlet equals to
. Turbine is a steady-flow system modelled by using Principle of Mass Conservation and First Law of Thermodynamics:
Principle of Mass Conservation
![\dot m_{in} - \dot m_{out} = 0](https://tex.z-dn.net/?f=%5Cdot%20m_%7Bin%7D%20-%20%5Cdot%20m_%7Bout%7D%20%3D%200)
First Law of Thermodynamics
![- \dot W_{out} + \eta\cdot (\dot m_{in} \dot h_{in} - \dot m_{out} \dot h_{out}) = 0](https://tex.z-dn.net/?f=-%20%5Cdot%20W_%7Bout%7D%20%2B%20%5Ceta%5Ccdot%20%28%5Cdot%20m_%7Bin%7D%20%5Cdot%20h_%7Bin%7D%20-%20%5Cdot%20m_%7Bout%7D%20%5Cdot%20h_%7Bout%7D%29%20%3D%200)
This 2 x 2 System can be reduced into one equation as follows:
![-\dot W_{out} + \eta \cdot \dot m \cdot ( h_{in}- h_{out})=0](https://tex.z-dn.net/?f=-%5Cdot%20W_%7Bout%7D%20%2B%20%5Ceta%20%5Ccdot%20%5Cdot%20m%20%5Ccdot%20%28%20h_%7Bin%7D-%20h_%7Bout%7D%29%3D0)
The water goes to the turbine as Superheated steam and goes out as saturated vapor or a liquid-vapor mix. Specific volume and specific enthalpy at inflow are required to determine specific enthalpy at outflow and mass flow rate, respectively. Property tables are a practical form to get information:
Inflow (Superheated Steam)
![\nu_{in} = 0.041767 \frac{m^{3}}{kg} \\h_{in} = 3399.5 \frac{kJ}{kg}](https://tex.z-dn.net/?f=%5Cnu_%7Bin%7D%20%3D%200.041767%20%5Cfrac%7Bm%5E%7B3%7D%7D%7Bkg%7D%20%5C%5Ch_%7Bin%7D%20%3D%203399.5%20%5Cfrac%7BkJ%7D%7Bkg%7D)
The mass flow rate can be calculated by using this expression:
![\dot m_{in} =\frac{\dot V_{in}}{\nu_{in}}](https://tex.z-dn.net/?f=%5Cdot%20m_%7Bin%7D%20%3D%5Cfrac%7B%5Cdot%20V_%7Bin%7D%7D%7B%5Cnu_%7Bin%7D%7D)
![\dot m_{in} = 23.942 \frac{kg}{s}](https://tex.z-dn.net/?f=%5Cdot%20m_%7Bin%7D%20%3D%2023.942%20%5Cfrac%7Bkg%7D%7Bs%7D)
Afterwards, the specific enthalpy at outflow is determined by isolating it from energy balance:
![h_{out} =h_{in}-\frac{\dot W_{out}}{\eta \cdot \dot m}](https://tex.z-dn.net/?f=h_%7Bout%7D%20%3Dh_%7Bin%7D-%5Cfrac%7B%5Cdot%20W_%7Bout%7D%7D%7B%5Ceta%20%5Ccdot%20%5Cdot%20m%7D)
![h_{out} = 1655.36 \frac{kJ}{kg}](https://tex.z-dn.net/?f=h_%7Bout%7D%20%3D%201655.36%20%5Cfrac%7BkJ%7D%7Bkg%7D)
The enthalpy rate at outflow is:
![\dot H_{out} = \dot m \cdot h_{out}](https://tex.z-dn.net/?f=%5Cdot%20H_%7Bout%7D%20%3D%20%5Cdot%20m%20%5Ccdot%20h_%7Bout%7D)
![\dot H_{out} = 39632.62 kW](https://tex.z-dn.net/?f=%5Cdot%20H_%7Bout%7D%20%3D%2039632.62%20kW)