Work

Thermodynamics

Professor Lee Carkner

Lecture 7

PAL # 6 Equations of State CO2 flow through a pipe

From Table A-1: R = 0.1889 kPa m3 / kg K Tcr = 304.2 K, Pcr = 7.39 MPa

V’1 = (2)(0.1889)(500) / 3000 = 0.06297 m3/s

V’2 = (2)(0.1889)(450) / 3000 = 0.05667 m3/s

1 = m’/V’ = 2/0.6297 =

2 = 2/0.05667 =

PAL # 6 Equations of State Use PR and TR to find Z from chart A-15

PR = P/Pcr = 3/7.39 =0.407 TR1 =500/304.2 = TR2 = 450/304.2 =

V’1 = (0.9791)(0.06297) = 0.06165

2.1% error 1 =32.44, error =2.1 % V’2 =(0.9656)(0.05667) = 0.05472

3.6% error 2 = 36.55, error =3.6 %

Exam #1

Friday, March 24th

Covers: Lectures 1-8 Chapters 1-4

Format: About 10 multiple choice (~25% weight) About 4 problems (~75%weight)

Equations provided Bring just pencil and calculator

Worth 15% of final grade

Work

No displacement, No work

We consider now external work Involves interaction with another system or its

surroundings (external to the system)

Work is a form of energy

Work and Hydrostatic Systems Work is not a property of the system

We need to be able to specify the properties of the system at each point in the process

Called a quasi-equilibrium or quasi-static process

Derivation of Work

Work, Pressure and Volume

W = F ds

W = P dV

If dV is positive (increase in V) then W is positive (work by the system)

Total Work

W = P dV Need to know P as a function of V

Often need to limit or parameterize T

W depends on both the change of volume and how the volume changed

PV Diagram

The process by which the volume changes is a line or curve connecting the two points

For different processes, different curves,

different amounts of work

Path Dependence of Work

Path Dependence What are the paths?

follow isotherm

horizontal

vertical

Closed Cycle

If the system moves from 1 to 2 and then back to 1, it is a cycle

if two different paths are traveled W is the area between the curves

Repeat the same process over and over,

extract work each cycle

Cycle Work

Polytropic Process

Often for compression and expansion of a gas, pressure and volume are related by:

Where C and n are constants

Called a polytropic process Can integrate between points 1 and 2:

For an ideal gas, can replace PV with mRT

Polytrope

Isothermal Process

W = C(1/V) dV = PV ln (V2/V1)

For an ideal gas PV = mRT so PV is constant

Piston of Air

Energy Balance

Qnet,in – Wnet,out =Esystem

Q – W = E First Law of Thermodynamics

We make a distinction between Q and W for eventual use with the second law

Specific Heat

The temperature change due to the energy change can be found with two specific quantities: Specific heat at constant volume

Specific heat at constant pressure

Units of kJ/kg K

cv and cP

Specific Energy

As energy is added to a system the rate of temperature change changes

c tells you the energy needed to effect a change

Temperature Dependence of c

Next Time

Read: 4.4-4.5 Homework: Ch 4, P: 36, 56, 74 Test 1 Friday