1. (25 points - no need for homework format) The approximation of calorific equation of state,i.e., h₂ h₁ = Cp,avg (T2-T₁), may be used to relate the change in mass-specific enthalpy to the change in temperature. However, this approximation is only applicable under certain scenarios.In this problem, you will think on the applicability regime of this approximation.In each of the following cases, provide the conditions under which h₂ h₁ = Cp,avg (T2-T₁)can be used (Note, if it is always applicable, state there is no additional requirement; If it is always inapplicable, state it never works; In other cases, explicitly state the condition)

a) The working fluid is an ideal gas.

b) Both State 1 and State 2 are sub cooled liquid.

c) Both State 1 and State 2 are liquid-vapor mixture.

d) Both State 1 and State 2 are super heated vapor, but not ideal gas. 2. (25 points) Text 8.2 Nozzle

Water enters a nozzle with a velocity of 0.8 m/s and exits with a velocity of 5 m/s. The nozzle entrance diameter is 12 mm. Estimate the inlet pressure, if the outlet pressure is 100 kPa and the water temperature is assumed to be the same at inlet and outlet as 300 K.Hint: you can consider the water in compressible. At 300 K, the density of water is 996.5 kg/m³. 3. (25 points) Text 8.21 Throttle

Saturated liquid water at 1 MPa enters a throttling device and exits at 0.2 MPa. Determine the temperature and quality of the exiting liquid-vapor mixture. Hint: Need use the energy balance relation for throttling device.

4. (25 points) Steam Power Plant

In a steam power plant, the rate of heat added in the boiler is 80 MW. The steam turbine generates 25 MW of shaft work. It is known that the steam enters at 10 MPa and 720 K, and exits at 6 kPa and 400 K.

a) Evaluate mass-specific enthalpy at the inlet of the turbine. Indicate which table you use.

b) Evaluate mass-specific enthalpy at the outlet of the turbine. Indicate which table you use. c) Determine the flow rate required to produce the 25 MW of shaft work from the steam turbine.

d) Evaluate the thermal efficiency for this steam power plant.

e) Evaluate the rate of heat transfer out from the condenser.