Department of Mechanical Engineering

ME 322 – Mechanical Engineering

Thermodynamics

Review for Exam 2

Exam Guidelines

• 50-minutes

• Resources allowed

– The blue properties booklet • You can write anything you

want in the white space of this booklet.

• NO photocopies, no taping, pasting, photocopies, or loose papers

– A handheld calculator • No other electronic devices may be

used including cell phones, computers, tablets, music players, etc.

2

Exam Information

• A table of conversion factors will be

provided with the exam

• NO interpolation will be required

• Material covered

– Everything since the first day of class

• All in-class lecture material

• All in-class problem solutions

• All assigned reading questions

• All homework assignments

3

Do you know ... • How to Identify Transport, Gain, and Production Terms

within the Laws of the Universe? – Conservation of mass

– Conservation of energy

– Entropy Balance

• How to apply the Continuity Equation along with the 1st Law of Thermodynamics in... – Closed system problems?

– Open system problems?

– Simple transient problems?

• The purpose of the following flow devices? – Diffuser, Nozzle

– Boiler, Condenser, Heat Exchanger

– Valves, Throttling Devices

– Turbine, Compressor, Pump

• How to find ideal gas properties with the air tables?

• How to find real fluid properties with tables and with EES?

• How to find properties of incompressible substances?

4

Do you know ... • How to use the caloric equation of state?

(for ideal gas enthalpy and internal energy)

• How to find the fluid velocity given mass flow, area, and either density or specific volume?

• What is meant by reversibility? What causes irreversibility?

• What is meant by entropy? What are its units?

• How to obtain reversible work and heat transfer from the first and second Gibbs equations? dU = TdS – pdV

dH = TdS + vdP

• Characteristic shape of isobars, isotherms, isentropes, and isochores on T-s diagrams?

• How to represent reversible work transfer for a closed system on P-v diagrams? How to represent reversible heat transfer for a closed system on T-s diagrams?

• How to use array tables in EES to organize state point data and superimpose thermodynamic processes on property diagrams?

5

Do you know ... • How to define the thermal efficiency for a cycle?

• How to define the coefficient of performance for a cycle?

• Kelvin-Planck statement of the 2nd Law?

• Clausius statement of the 2nd Law?

• How to determine the maximum thermal efficiency of a heat engine?

• How to determine the maximum coefficient of performance for a refrigerator?

• How to determine the maximum coefficient of performance for a heat pump?

• How to determine entropy changes for substances using real fluid, ideal gas, and incompressible substance models?

• The polytropic relationships for the special case of ideal gases with constant heat capacity undergoing isentropic processes?

6

The Laws of the Universe

7

2 2

2 2

sysi ei i i e e e

i ec c c c

dEV Vg gQ W m h z m h z

g g g g dt

sys

i e

i e

dmm m

dt

Conservation of Mass – The Continuity Equation

Conservation of Energy – The First Law of Thermodynamics

The Entropy Balance – The Second Law of Thermodynamics

syski i e e P

k i ek

dSQm s m s S

T dt

Alternate Forms: 1st Law for Closed Systems

8

2 2

2 1 2 1 2 12 c c

m mgQ W U U V V z z

g g

2 2

2 1 2 1

2 12 c c

V V g z zq w u u

g g

The First Law over a finite period of time is (making a movie),

The First Law at an instant in time is (taking a picture),

2

2

sys

c c

dE d mV mgzQ W U

dt dt g g

T GE E sysdE

dt

Caloric Equation of State – Ideal Gas

9

For an ideal gas,

vdu c dT

Since we are dealing with an ideal gas, pv = RT. Therefore,

h u pv h u RT h h T

This leads to the following conclusion (section 3.9.2),

pdh c dT

It can also be shown that,

p vc c R

The Polytropic Process – Ideal Gas

10

Definition of a polytropic process: 2 1

1 2

n

p V

p V

If the fluid is an ideal gas,

2 1 1 1

1 2 2 2

/

/

n

p V mRT p

p V mRT p

This leads to two additional relationships for ideal gases,

1 / 1

2 2 2 2

1 1 1 1

and

n n n

T p T V

T p T V

The Polytropic Process – Ideal Gas

11

2

1

1 1 2 2 1 112 for 1

1

nV

nV

p V p V p VW dV n

V n

The work done during a polytropic process is,

If the fluid is an ideal gas,

2 1

12 for 11

mR T TW n

n

2

1

1 1 212 1 1

1

lnV

V

p V VW dV p V

V V

For the case where n = 1,

Ideal Gas Entropy f(T,V)

For the ideal gas, recall that

, ,v pPv RT du c dT dh c dT and

2 2 2 2 2

1 1 1 1 1

22 1

1

lnu v T v T

v vu v T v T

vdu P dT RT dv dTs s dv c c R

T T T v T T v

Then from the first Gibbs equation,

Furthermore, if the heat capacity can be assumed constant,

2 22 1

1 1

ln lnv

T vs s c R

T v

Notice that the entropy of an ideal gas is a function of both

temperature and specific volume (or pressure).

12

2 2 2 2 2

1 1 1 1 1

22 1

1

lnh P T P T

p ph P T P T

Pdh v dT RT dP dTs s dP c c R

T T T P T T P

Ideal Gas Entropy f(T,P)

For the ideal gas, recall that

, ,v pPv RT du c dT dh c dT and

Then from the second Gibbs equation,

Furthermore, if the heat capacity can be assumed constant,

2 22 1

1 1

ln lnp

T Ps s c R

T P

Notice that the entropy of an ideal gas is a function of both

temperature and pressure.

13

Carnot Heat Engine

14

1cycle in out out

th

in in in

W Q Q Q

Q Q Q

Kelvin and Rankine suggested that,

out L

in Hrev

Q T

Q T

Therefore, the thermal efficiency of a Carnot Heat Engine is,

, 1 Lth Carnot

H

T

T

Temperatures must be

on the absolute scale! LT

HT

This is the maximum

efficiency of a heat engine!

, 1cycle in out out

th Carnot

in in in rev

W Q Q Q

Q Q Q

Carnot Refrigerator & Heat Pump

15

R

1COP

/ 1

in inth

out in out incycle

Q Q

Q Q Q QW

For the Refrigeration cycle …

H

H, H,

1COP

1 /

1 1COP COP

1 /1 /

out out

th

out in in outcycle

HCarnot Carnot

L H H Lin out rev

Q Q

Q Q Q QW

T

T T T TQ Q

For the Heat Pump cycle …

HT

LT

R,

1 1COP

/ 1/ 1Carnot

H Lout in revT TQ Q

R,COP LCarnot

H L

T

T T