Short Answer:

The first law of thermodynamics applies to turbines by explaining how energy is conserved as heat and work are exchanged. In a turbine, high-pressure fluid enters and expands, doing mechanical work on the rotating shaft. The law helps calculate how much energy is converted from fluid energy into useful work output.

In turbines, the heat transfer is often negligible, so the energy change mainly comes from the decrease in the enthalpy of the fluid. The first law provides the basis for determining the shaft work produced by the turbine and helps engineers design efficient energy conversion systems.

Detailed Explanation:

First law of thermodynamics in turbines

The first law of thermodynamics, also known as the law of energy conservation, states that energy can neither be created nor destroyed, only transformed from one form to another. When applied to turbines, this law helps us understand how thermal or fluid energy is converted into mechanical work.

A turbine is a mechanical device that extracts energy from a high-pressure fluid (such as steam, gas, or water) and converts it into rotational work. This work is then used to run generators, pumps, or other mechanical equipment.

Energy Conversion in a Turbine

In a turbine, fluid enters at high pressure and velocity and exits at a lower pressure. As the fluid expands, it passes over blades connected to a shaft. The moving fluid transfers energy to the blades, causing the shaft to rotate. This rotation is the mechanical work output of the turbine.

The first law of thermodynamics in a steady-flow process like a turbine is written as:

Q̇ – Ẇ = ṁ × (h₂ – h₁ + (V₂² – V₁²)/2 + g(Z₂ – Z₁))

Where:

• Q̇ = Heat transfer rate
• Ẇ = Shaft work done by the turbine
• ṁ = Mass flow rate of fluid
• h = Specific enthalpy
• V = Velocity of fluid
• Z = Elevation (height)
• g = Gravitational constant

In many turbine applications, heat transfer (Q̇) and potential energy (Z terms) are negligible, so the equation simplifies to:

Ẇ = ṁ × (h₁ – h₂ + (V₁² – V₂²)/2)

This means the work output depends mainly on the drop in enthalpy and kinetic energy between the inlet and outlet of the turbine.

Important Points in Turbine Analysis

1. Enthalpy drop provides energy:
   The decrease in enthalpy (h₁ – h₂) represents the usable energy that is converted into work.
2. Steady-flow assumption:
   Most turbines operate under steady-flow conditions, where properties remain constant over time.
3. Negligible heat loss:
   Turbines are usually insulated, so heat loss to the surroundings is minimal and often ignored in basic calculations.
4. Mass flow continuity:
   The mass of fluid entering the turbine equals the mass exiting it (ṁ_in = ṁ_out), assuming no leaks.
5. Work output per unit mass:
   Specific work output (per kg of fluid) is directly calculated from the energy balance using enthalpy and velocity terms.

Application in Real-Life Turbines

• Steam Turbines:
  Used in thermal power plants where steam expands through multiple stages, causing blades to rotate and produce electricity.
• Gas Turbines:
  Used in jet engines and power stations, where high-temperature gas rotates the turbine shaft.
• Hydraulic Turbines:
  Used in hydroelectric power plants where water flows through turbines and converts potential energy into mechanical work.

In all these turbines, the first law helps calculate how much input energy is being converted into shaft work and how efficiently the turbine operates.

Efficiency and Energy Losses

Though the first law tells us energy is conserved, it doesn’t tell us how much of that energy is useful. In real turbines, there are friction losses, leakages, and turbulence, so not all the enthalpy drop converts to work. The efficiency of a turbine is defined by comparing actual work output to the ideal work (from the first law).

Conclusion

The first law of thermodynamics is directly applied to turbines by balancing the energy entering and leaving the system. In a turbine, high-pressure fluid expands and performs mechanical work, which is calculated using enthalpy and velocity changes. This principle is essential in designing, analyzing, and improving the performance of all types of turbines used in power generation and mechanical systems.