Question

According to First law of thermodynamics for a flow process the total work done by the turbine can be approximated by______

• A. the enthalpy change of the steam
• B. the entropy change of the steam
• C. free energy change of the steam
• D. kinetic energy change of the steam

Hint:

For any open-flow expansion device (turbine) or compression device (compressor/pump), if kinetic and potential energy changes are neglected and the system is adiabatic, the work is always equal to the change in enthalpy.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the thermodynamic approximation of the work done by a steam turbine in an open flow system, using the First Law of Thermodynamics.
This falls under the open-system (control volume) energy analysis.

Step 2: Key Formula or Approach:
The steady-flow energy equation (SFEE) for a control volume with a single inlet and outlet is:
\[ \dot{Q} - \dot{W}_s = \dot{m} \cdot \left[ \Delta h + \frac{\Delta v^2}{2} + g \cdot \Delta z \right] \]
where:
\( \dot{Q} \) is heat transfer rate,
\( \dot{W}_s \) is shaft work done by the system,
\( \dot{m} \) is mass flow rate,
\( \Delta h \) is change in specific enthalpy,
\( \frac{\Delta v^2}{2} \) is change in kinetic energy,
\( g \cdot \Delta z \) is change in potential energy.

Step 3: Detailed Explanation:

• Turbine Assumptions:
1. A turbine is typically assumed to be adiabatic, meaning heat loss is negligible: \( \dot{Q} \approx 0 \).
2. The changes in kinetic energy (\( \Delta KE \)) and potential energy (\( \Delta PE \)) of steam between the inlet and exit are usually small compared to the large change in enthalpy.
\[ \Delta KE \approx 0, \quad \Delta PE \approx 0 \]

• Simplification:
Applying these assumptions to the SFEE yields:
\[ - \dot{W}_s = \dot{m} \cdot \Delta h \]
\[ W_{\text{shaft}} = - \Delta H \]
This demonstrates that the work produced by the turbine is equal to the drop in enthalpy of the fluid as it expands through the stages.


Step 4: Final Answer:
The total work done by the turbine is approximated by the enthalpy change of the steam.