Math Problem Statement

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A steam turbine generates an electrical equivalent of 800 kW in a coal-based power plant. Assume the steam enters a turbine with a velocity of 40 m/s and enthalpy is 2900 kJ/kg. The steam leaves the turbine at a mixture of vapor and liquid, having a velocity of 60 m/s and an enthalpy of 2500 kJ/kg. Determine the work output provided per unit mass of steam if the flow through the turbine is considered to be adiabatic, and changes in elevation are negligible.

Solution

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Energy balance
Adiabatic processes
Enthalpy

Formulas

First law of thermodynamics for open systems: ΔH + ΔKE + ΔPE = W
Work output per unit mass: W = (h1 - h2) + (v1^2 - v2^2)/2

Theorems

Conservation of energy

Suitable Grade Level

Undergraduate Engineering

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