In which component is the energy balance described by w = h2 - h1?

In which component is the energy balance described by w = h2 - h1?

• A. Pump
• B. Boiler
• C. Turbine
• D. Condenser

Answer: (A)

When a steady-flow device has no heat transfer and negligible changes in kinetic and potential energy, the shaft work put into or out of the fluid is directly tied to how the fluid’s enthalpy changes. In that situation the energy balance simplifies to the work per unit mass equal to the change in specific enthalpy: w = h2 − h1. This is exactly what happens in a pump. The motor delivers shaft work to the liquid, and the only energy transfer that matters for the fluid is this work input, so the fluid’s enthalpy rises by the amount of work added. Hence the work input per unit mass equals the enthalpy rise, w = h2 − h1. Other devices involve energy transfer mainly as heat or, in the case of a turbine, the fluid does work on surroundings and its enthalpy decreases. In a boiler, heat transfer raises enthalpy (h2 − h1 is related to heat added, not shaft work). In a turbine, the fluid’s enthalpy drops as it performs work, so the sign would reflect a decrease in enthalpy (and the relationship to shaft work would have a different form). In a condenser, heat is rejected, again changing enthalpy primarily through heat transfer rather than shaft work.

When a steady-flow device has no heat transfer and negligible changes in kinetic and potential energy, the shaft work put into or out of the fluid is directly tied to how the fluid’s enthalpy changes. In that situation the energy balance simplifies to the work per unit mass equal to the change in specific enthalpy: w = h2 − h1.

This is exactly what happens in a pump. The motor delivers shaft work to the liquid, and the only energy transfer that matters for the fluid is this work input, so the fluid’s enthalpy rises by the amount of work added. Hence the work input per unit mass equals the enthalpy rise, w = h2 − h1.

Other devices involve energy transfer mainly as heat or, in the case of a turbine, the fluid does work on surroundings and its enthalpy decreases. In a boiler, heat transfer raises enthalpy (h2 − h1 is related to heat added, not shaft work). In a turbine, the fluid’s enthalpy drops as it performs work, so the sign would reflect a decrease in enthalpy (and the relationship to shaft work would have a different form). In a condenser, heat is rejected, again changing enthalpy primarily through heat transfer rather than shaft work.