Superheated steam at 40 bar absolute and 500°c flows at a rate of 250 kg/min to an adiabatic turbine, where it expands to 5 bar. the turbine develops 1500 kw. from the turbine the steam flows to a heater, where it is reheated isobarically to its initial temperature. neglect kinetic energy changes. a. write an energy balance on the turbine and use it to determine the outlet stream temperature. (7 marks) b. write an energy balance on the heater and use it to determine the required input power (kw) to the steam. (6 marks) c. verify that an overall energy balance on the two-unit process is satisfied. (6 marks) d. suppose the turbine inlet and outlet pipes both have a diameter of 0.5 meter. show that it is reasonable to neglect the change in kinetic energy for this unit

a.

b.

c. See explanation.

d. Its result is not significant in comparison with the involved enthalpies and the produced work (see explanation).

Explanation:

Hello,

a. In this case, as superheated steam enters to the turbine, the energy balance for the given mass rate is:

At 40 bar and 500 °C, the corresponding enthalpy is 3446.0kJ/kg, therefore, the enthalpy at the outlet is:

Now, at 5 bar and 3086 kJ/kg, the temperature corresponds to the temperature of a supersaturated vapor as well, thus interpolating from Cengel's table A-6, the outlet temperature is 306.78 °C.

b. Afterwards, the heat required at the heater involves just sensible heat from 306.78 °C to 500 °C whose difference implies that polynomial heat capacity must be used, therefore, the heat is computed via:

The values for water given in Cengel are in kJ/kmol, therefore, a conversion  is done by using its molar mass, thus:

c. Then, an overall energy balance is:

In this case, equal the inlet enthalpy in the a. section, was computed in the previous section and is given in the statement, just is computed as follows, considering that at 5 bar and 500 °C the water is steam:

Therefore, the energy balance is satisfied as shown below:

It is seen that both of the sides are roughly the same, therefore, the energy balance is satisfied.

d. Finally, since kinetic energy is defined as:

Whereas is the fluid velocity, it could be computed by considering the specific volume extracted from the same tables at the entrance and the exit of the turbine which are:

Now, the velocities are:

Therefore, the change in kinetic energy is:

Summing it up, such result is not significant in comparison with the involved enthalpies and the produced work, in such a way, it is reasonable to neglect it along the calculations.

Best regards.

b.

the accuracy of the data.