Lec 11: Flow work, energy transport by mass, first law of thermodynamics

For next time: Outline: Important points: Read: § 5-2 to 5-3 HW 6 due Wednesday, October 8, 2003 Outline: Flow work Conservation of energy Open and closed systems Important points: Know how to calculate start and end states Know how to find the path between states Know when to apply the various forms of the conservation of energy equation

Flow work For open systems, obviously work must be done to move the fluid into and out of the control volume. It is a form of boundary work. L Flow “piston” of fluid having m, P, V. A is crossectional area of pipe.

Flow work The force on the fluid element F=PA But AL is V, so W=PV or

Energy of fluid in closed system Energy of a simple, compressible system is

Energy of fluid in open system Now there is a fourth term: the flow energy Where Pv + u is just h, so

Energy transport by mass Now that we know the energy per unit mass =h+ke+pe for an open system, the energy transported in and out with the mass is just the product of the mass and the energy:

Conservation of Energy First Law of Thermodynamics The net change (increase or decrease) in the total energy (Esystem) of a system during a process is equal to the difference between the total energy transferred in or entering (Ein) and the total energy transferred out or leaving the system during that process.

Conservation of Energy First Law of Thermodynamics For a simple, compressible system, and a change in E is

The kinetic energy is given by: To what does this kinetic energy term apply ? Explain to the person across the table.

Energy has units of force times distance Energy has units of force times distance. The energy change in accelerating a mass of 10 kg from Vi= 0 to Vf = 10 m/s is?

NOTE THE CONVERSION TO GET FROM m2/s2 to kJ/kg REMEMBER IT! YOU WILL NEED IT.

TEAMPLAY How much energy in ft lbf must a shot putter exert in throwing a 16 lbm shot put if it is released at 30 ft/s? How does this compare to a 60 W light bulb burning for 10 sec?

Gravity is another force acting on our system Gravity is another force acting on our system. It shows up in the potential energy change. Work can be done by a change in elevation of the system.

TEAMPLAY Let’s say we have a 10 kg mass A that we drop 100 m. We also have a device that will convert all the potential energy of A into kinetic energy of an object B. If the mass of object B is 1 kg and it is initially at rest, what would be B’s final velocity from absorbing the potential from a 100 m drop of A? Assume that object B travels horizontally.

Internal energy….. Internal energy is the energy a molecule possesses, mostly as a result of. Translation Vibration Rotation All these are forms of kinetic energy. We will neglect other forms of molecular energy which exist on the atomic level.

Conservation of Energy First Law of Thermodynamics Energy can be transferred into (or out of) the system in three ways: Heat interactions (called heat transfer) Work interactions Mass flow (carrying energy with the mass).

Conservation of Energy First Law of Thermodynamics Viewed in this way, E on the right hand side is a property of the system. However, the left side has Q and W which depend on the path, in general. This leads us to sometimes write

Conservation of Energy First Law of Thermodynamics Adiabatic means simply that there is no heat transfer, or Q=0. Consider a closed, adiabatic system. adiabatic closed

Conservation of Energy First Law of Thermodynamics Now we have or in differential form

Conservation of Energy First Law of Thermodynamics So for an adiabatic closed system the work is equal to a path independent quantity, which means adiabatic work is independent of path. This is another form of the first law; “For all adiabatic processes between two specified states of a closed system, the work is the same, regardless of the nature of the closed system and the details of the process.”

TEAMPLAY Is an adiabatic process the same as a constant temperature process? Explain to the teammate next to you why or why not - try to think of some examples.

Conservation of Energy First Law of Thermodynamics Let us replace Qin- Qout by a single Q that represents the sum of all heat interactions during the process. Remember--if heat is transferred in it is positive--if transferred out it is negative.

Conservation of Energy First Law of Thermodynamics Let us replace Win- Wout by a single -W that represents the sum of all work interactions during the process. Remember--if work is done on the system it is negative. If done by the system, it is positive.

Conservation of Energy First Law of Thermodynamics The first law is now simply Note that heat transferred to the system (+) or work done on the system (-) both will raise the energy of the system.

So let’s put it all together again: This is the algebraic statement of the first law for closed systems of all kinds, not just adiabatic.

Conservation of Energy First Law of Thermodynamics Stationary means not moving--so PE and KE are zero and the first law becomes

TEAMPLAY Solve problem 5-15.

Energy analysis of cycles For the cycle, E1- E1 = 0, or

For cycles, we can write: Qcycle = Wcycle, Qcycle and Wcycle represent net amounts which can also be represented as:

TEAMPLAY A closed system undergoes a cycle consisting of two processes. During the first process, 40 Btu of heat is transferred to the system while the system does 60 Btu of work. During the second process, 45 Btu of work is done on the system. Determine the heat transfer during the second process. Determine the net work and net heat transfer of the cycle.

TEAMPLAY Solve problem 5-47