1 Lec 3: Conservation of mass continued, state postulate, zeroth law, temperature

2 For next time: –Read: § 10-1 to 10-2, 10-4 to 10-5, and 2-5 to 2-8. Outline: –Conservation of mass example problems –Equilibrium and states –Zeroth law of thermodynamics Important points: –Problem solving methodology –State, path, and process –Temperature scales

3 Review where and

4 Steady flow Flows are steady if any derivative with respect to time equals zero: The term steady state may also be used, which simply means that any property (used to define a state) does not vary with time, although they may vary with position.

5 Conservation of mass OR If we limit ourselves to steady-state devices with one entrance and one exit,

6 Look at some simplifying cases: Incompressible pipe flow: General Incompressible:

7 One more simplifying case: Ideal gas incompressible:

8 TEAMPLAY Steam enters a turbine with a specific volume of ft 3 /lb m with a velocity of 21.0 ft/s and leaves with a specific volume of ft 3 /lb m. The turbine inlet area is 1 ft 2 and the outlet area is 140 ft 2. A) What is the mass flow (lb m /hr)? B) What is the exit velocity (ft/s)?

9 Review--State The state of a system is defined by the values of its properties.

10 TEAMPLAY How many properties can you name that apply to the gas in a high pressure cylinder of nitrogen? How many are independent and how many are dependent?

11 Equilibrium A system is in equilibrium if its properties are not changing at any given location in the system. This is also known as “thermodynamic equilibrium” or “total equilibrium.” We will distinguish four different subtypes of thermodynamic or total equilibrium.

12 Types of thermodynamic equilibrium: Thermal equilibrium--temperature does not change with time. Mechanical equilibrium--Pressure does not change with time. Phase equilibrium--Mass of each phase is unchanging with time. Chemical equilibrium--molecular structure does not change with time.

13 Equilibrium Equilibrium implies balance--no unbalanced potentials (driving forces) in the system.

14 State Principle or State Postulate Text says, “The state of a simple compressible system is completely given by two independent, intensive properties.” Properties are independent if one can be constant while the other varies. This only applies at equilibrium.

15 Process Change in state of a system from one equilibrium state to another.

16 Path Series of states through which a system passes.

17 Properties at end points are independent of the process

18 Constant property processes The prefix “iso” is used to indicate a property that remains constant during a process: –Isothermal is constant temperature –Isobaric is constant pressure –Isochoric or isometric is constant volume

19 Review definitions Steady state--any property (used to define a state) does not vary with time, although it may vary with position. Compare with definition of equilibrium. A system is in equilibrium if its properties are not changing at any given location in the system. So, the question arises: how does something change with time?

20 Quasiequilibrium Process Idealized process in which the departure from equilibrium is infinitesimally small. Gas or liquid system Boundary Incremental masses removed during an expansion of the gas or liquid

21 Quasiequilibrium Processes Engineers are interested in quasiequilibrium processes for two reasons: –They are easy to analyze because many (relatively) simple mathematical relations apply. –It will be shown later that devices produce maximum work or require minimum work when they operate on quasiequilibrium processes.

22 Cycle Series of processes where the initial and final states are the same.

23 State Principle (more rigorous definition) The number of independent, intensive properties needed to characterize the state of a system is n+1 where n is the number of relevant quasiequilibrium work modes. This is empirical, and is based on the experimental observation that there is one independent property for each way a system’s energy can be independently varied.

24 State Principle continued The “1” is for heat transfer (Q). The “n” is the number of relevant quasiequilibrium work modes. In this course, we will usually have n = 1.

25 Simple system A simple system is defined as one for which only one quasiequilibrium work mode applies.

26 For a simple system, We may write:p = p(v,T) Or perhaps: v = v(p,T).

27 Forms of Energy Energy is usually symbolized by E, representing total energy e is energy per unit mass

28 Forms of Energy Macroscopic forms--possessed with respect to some outside reference frame. –Kinetic energy, –Potential energy,

29 Forms of energy Microscopic forms are called internal energy (internal to the molecule) and represent the energy a molecule can have as it translates, rotates, and vibrates. There are other contributors--nuclear spin, for example--as well. We will not concern ourselves with the details, but will use the symbols U and u.

30 Energy Now, we have and for stationary, closed systems, KE and PE are 0. So, for stationary closed systems, E= U

31 Energy Sensible energy--the portion of the internal energy associated with all forms of kinetic energy of the molecules. Latent energy--refers to internal energy associated with binding forces between molecules. Phase changes, such as vaporizing (boiling) water are latent energy changes.

32 Thermal Equilibrium Occurs when two bodies are at the same temperature T and no heat transfer can occur.

33 Zeroth Law of Thermodynamics If two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other.

34 Boiling point ºC ºF K R Triple atm, T = 0.01 ºC Ice point Absolute Zero We Need to Work With Temperatures

35 Temperature relationships T (ºR) = T (ºF) [use 460] T (K) = T (ºC) [use 273]