MDME: MANUFACTURING, DESIGN, MECHANICAL ENGINEERING

# CLOSED SYSTEMS

A thermodynamic system can be defined as a boundary chosen for the analysis of a problem. It can be either a quantity of matter (closed system) or a region of space (open system).

SmartBoard Notes: Closed Systems.pdf Closed Systems.one

 Type Video Lesson Description and Link Duration Date Worked problem W=p V: Calculating the work of moving a piston 5 min 20200506 Worked problem VL-10903b: Internal Energy: U=Q-W: 14MB 10 min 20091106 Worked problem VL-10903c: Internal Energy: U=mC T: (4 Worked examples): 15MB 15 min 20091107 Worked problem VL-10903d: Isolated Systems: U=0: (2 Worked examples) 17MB 13 min 20091108

## System Definitions

• Isolated system:  No mass transfer and no energy transfer across the system boundary.
• Closed system:  No mass transfer, but energy may transfer across the system boundary.
• Open system:  Both mass and energy allowed to transfer across the system boundary.
• ## Internal Energy U

Internal Energy U

Internal energy U is the energy associated with the random motion of molecules.

The symbol is U, units are Joules (J). It depends on the temperature, the mass, the type of molecules and how they interact (e.g. solid vs liquid).

At zero temperature (0K or -273.15oC) there is no internal energy (U=0), which means the atoms are motionless, This is why everything is a solid (except Helium perhaps).

See melting points on Interactive Periodic table here (off-site); http://www.dayah.com/periodic/ The kinetic energy of a molecule is more than just velocity. It can be a combination of all the degrees of freedom of the structure.

More Examples: Kinetic theory of gases: (Java) Perfect Gas Simulator (Java)

## Closed Systems

A closed system has no mass transfer, but allows energy transfer across the system boundary. Closed systems are also called non-flow systems, control-mass systems or constant-mass systems. A solid is a closed system (no mass transfer across boundary) Expanding or compressing a gas can also be a closed system if there is no flow or major leakages.

Non-flow Energy Equation (1st Law of Thermodynamics);

U2-U1 = Q - W
Where
U = internal energy (J)
Q = heat transfer (J) (+ = heat IN)
W = work transfer (J) (+ = work OUT)

WARNING! The (Kinsky) book uses this definition U2-U1 = Q - W. (i.e. Positive work is work done BY the system (not To the system which is more consistent with the concept of a Free Body Diagram)  See Ref 1

Confused?  Just remember...          Expansion =  Positive Work !

Internal Energy Change  = heat in + work in General Closed System showing work (W) and heat (Q) transfer

Non-flow, No phase change, Constant c;      U2-U1 = mc t
Where
U = internal energy (J)
m = mass (kg)
c = specific heat capacity (J/kgK) t= (t2-t1) = (tfinal-tintitial) = temperature change (K or oC)

Non-flow, With phase change, Constant c;      U2-U1 = mc1(t1-t0) + mcphaset1 + mc2(t2-t1)
t0 = initial solid temperature
t1 = fusion temperature (melting/freezing)
t2 = final liquid temperature
(For example, melting ice....
Energy change (or heat added) = (heat ice from ? to 0oC) + (latent heat of fusion) + (Heat water to ?oC)

## Isolated Systems

No mass transfer and no energy transfer across the system boundary, but only transfer between bodies within the system. Isolated (Insulated) System:   U = constant
Since there is no mass change, Q = 0

Finding Equilibrium Temperature: T
From Q = 0
Qw + Qb = 0
mwcw(T-Tw) = - mbcb(T-Tb)
T =  (mwcwTw + mbcbTb) / (mwcw + mbcb)

## Examples   Here is a bit more detail on the double negative in the outboard motor question.

The 35.1MJ of work we calculated is a negative work because it is being applied TO the system.

Now put this into the first law of thermo: U2-U1 = Q - W = 0 - (-35.1) = +35.1 MJ

Also notice the use of this equation, U2-U1 = mc t

It says that the change of internal energy is found by the change in temperature.

We can pretty much use this equation for every problem EXCEPT gases inside a piston (where expansion or contraction alters the internal energy, not just temperature). We always have to take temperature into account, but when there is expansion or contraction, we must account for this using W=p V. We will do this in the Gases chapter.   ## Questions:

Homework Assignment: Kinksy new edition
Do all questions; Chapter 4: Closed and Open Systems
4.1 to 4.11 (page 86 - 87)

Do all questions. Similar to quiz.
##### References and Notes
1. This important equation (1st Law of Thermodynamics) is written both ways in different books - Physics books are the same as our text (Kinsky), Chemistry books us the other defnition. Essentially all modern textbooks of physical chemistry use U=Q+W, such as those by Peter Atkins and Ira Levine, but all textbooks on physics (including Kinksy) define work as U=Q-W, the work done by the system - which is surprisingly contrary to the concept of the Free Body Diagram (Where signs are determined by what is done "TO THE BODY"). I prefer the Chemistry way, but we will stick to the textbook to avoid confusion.
##### Relevant pages in MDME Ice-in-box.onepkg Ice-in-box.pdf