Question $1$

Energy transfer mechanisms play key roles in Engineering. The energy balance equation finds many applications in

designing systems and processes. For example, the energy balance equation is applied to estimate the velocity of steam

leaving a nozzle, the rate at which heat must be added to a water boiler, or how much shaft work the turbine of a

geothermal power station produces.

Your task:

Look around your home, or neighborhood or be inspired by a past road trip, and identify a system or process that

converts energy from one form into another.

After identifying a system or process, derive a simplified energy balance equation that shows how the system or

process transforms one form of energy into another. ${?}^{****}$ Here is an example darr.${?}^{****}$

We recommend keeping it simple and within the scope of ENGGEN $140.$

We also recommend a systematic strategy for applying the energy balance:

Identify a system that has clearly recognizable boundaries or define its boundaries.

Go through each form of energy represented in the generalized energy balance $($e$.$g$.,$ work, heat, potential energy,

kinetic energy$)$ and carefully consider whether it is negligible or significant for the chosen system. Simplify the

equation by setting the negligible terms to zero with justification $($i$.$e$.,$ state your assumptions$).$

For those equation terms which are, or may be$,$ significant, determine a strategy for relating them to the known

information. For example, substitute $E$ pot with $mgh$ and exchange the variables with actual numbers and units.Question $2$

A conventional thermal power plant such as Huntly Power Station in the Waikato $G$ generates electricity by burning gas

or coal to drive turbines with superheated steam. Before entering the steam turbine, nozzles convert some of the thermal

energy in the superheated steam into kinetic energy, spinning the turbine blades.

You want to analyse the following problem:

An adiabatic nozzle accelerates superheated steam at steady$-$state conditions $($seel schematic illustration below$).$

The steam entering the nozzle has an energy content of $3273\mathrm{.}3kJ$ per $kg$ of steam $(=$ sum of internal energy and flow

work, at a pressure of $0\mathrm{.}5$MPa and $400C).$ The velocity of the steam entering the nozzle is negligible compared to that of

the steam exiting. The steam exiting the nozzle contains $3175\mathrm{.}8kJ$ of energy per $kg$ of steam $(=$ sum of internal energy and

flow work, at a pressure of $0\mathrm{.}1$MPa and $350C).$

What is the steam's exiting velocity? State your assumptions.

${?}^{****}$ Hot tip: Derive a simplified energy balance for this system $($see Question $1$ above$),$ using the simplifying assumptions stated. ${?}^{****}$