ENGR 260Section 6.5 – 6.8

Heat Engine Heat Pump Refrigerator

H

L

H

outnet

Q

Q

Q

W 1,

LH

L

innet

LR QQ

Q

W

QCOP

,H

L

QQ

innet

HHP W

QCOP

1

1

,

Kelvin-Planck Statement

• The Second Law of Thermodynamics– It is impossible for any device that operates

on a cycle to receive heat from a single reservoir and produce a net amount of work.

Kelvin Planck Statement

• Heat Engine must have a low temperature sink!

Clausius Statement of Second Law

• It is impossible to construct a device that operates in a cycle and produces no effect other than to transfer heat from a low temperature body to a higher temperature body.

Clausius Statement

• Heat Pumps and Refrigeration must have work input!

Perpetual Motion Machines

Two Types:

• PMM1 ~ violates the first law of thermo

• PMM2 ~ violates the second law of thermo

• Some PMMs actually violate both laws

Perpetual Motion Machines

• PMM1 ~ violates the first law of thermo

Perpetual Motion Machines

• PMM2 ~ violates the second law of thermo

Perpetual Motion Machines

Perpetual Motion Machines

Perpetual Motion Machines

Quiz for Tuesday:

Find an example of a perpetual motion machine

Show it in class Tuesday

Explain if it is a PMM1 or PMM2

• Reversible process ~ a process that can be reversed without leaving any trace on the surroundings– the system and the surrounding are returned

to their initial state– net work and heat exchange between process

and surrounding is zero for the combined process

Reversible and Irreversible Processes

Reversible Processes

Reversible Processes

Reversible Processes

Can a reversible process really occur?

No!

So why study them?

1) They are easy to analyze.

2) They are idealized models to predict theoretical limits of corresponding actual processes.

Reversible Processes

• Deliver the most

• Consume the least work

• Reversible process ~ a process that can be reversed without leaving any trace on the surroundings– the system and the surrounding are returned

to their initial state– net work and heat exchange between process

and surrounding is zero for the combined process

Reversible and Irreversible Processes

Irreversibilities

• Friction

• Unrestrained expansion of a gas

• Mixing of two fluids

• Heat transfer through a finite temp differential

• Electric Resistance

• Inelastic deformation of solids

• Chemical Reactions

Friction

Energy supplied as work is converted to heat.

Heat is transferred to bodies in contact.

This is seen as a temperature rise.

When reversed heat is not converted back to work.

Unrestrained expansion of a gas

Only way to restore system:

Compress to initial volume

Transfer heat from gas to return to original temperature

Involves transferring heat to work which violates 2nd law

Heat Transfer

Violates 2nd Law

Clausius Statement – cannot transfer heat from low temp body to high temp body without work

Clausius Statement

• Heat Pumps and Refrigeration must have work input!

Internally/Externally Reversible

• Internally Reversible:– No irreversibilities occur within system

boundaries (quasi-equilibrium)

• Externally Reversible:– No irreversibilities occur outside system

boundaries

• Totally Reversible:– No irreversibilites occur within system or its

surroundings

Chapter 5 Example

An adiabatic air compressor is to be powered by a direct-coupled adiabatic steam turbine that is also driving a generator. Steam enters the turbine at 12.5 MPa and 500oC at a rate of 25 kg/s and exits at 10 kPA and a quality of 0.92. Air enters the compressor at 98 kPa and 295 K at a rate of 10 kg/s and exits at 1 Mpa and 620 K. Determine the net power delivered to the generator by the turbine.

Mass flow = 10 kg/sec Mass flow = 25 kg/sec

Quality = 0.92

hair in = 295.17 kJ/kg (Table A-17)

hair out = 628.07 kJ/kg (Table A-17)

hwater out = 2392.5 kJ/kg (Table A-5)

hsteam in= 3343.6 kJ/kg (Table A-6)

Heat Engine Review

• Heat engines are cyclic devices in that the working fluid returns to it original state at the end of each cycle. – Work is done by the fluid in part of the cycle

and on the fluid during another part of the cycle.

– Efficiency of a cycle is dependent on the processes that make up a cycle.

– Efficiency can be maximized by using reversible processes.

Carnot Cycle

• Proposed by a French engineer Sadi Carnot in 1824

• Theoretical heat engine

• Comprised of four reversible processes. 2 isothermal and 2 adiabatic

Carnot Cycle

• Consider a closed system containing gas in an adiabatic piston-cylinder assembly.

Reversible Isothermal Expansion

– Process 1-2

– TH is constant.

– Cylinder head in close contact with source at TH

– Gas expands slowly doing work on surroundings

– Reversible heat transfer process

– Amount of heat transferred is QH

Reversible Adiabatic Expansion

– Process 2-3– Reservoir is removed, replaced with insulation– Gas expands doing work on surroundings

– Temp drops from TH to TL

– Frictionless piston and quasi-equilibrium – Reversible and adiabatic

Reversible Isothermal Compression

– Process 3-4

– TL is constant.

– Cylinder head in close contact with sink at TL

– Piston is pushed with external force doing work– Reversible heat transfer process

– Amount of heat rejected is QL

Reversible Adiabatic Compression

– Process 4-1– Reservoir is removed, replaced with insulation– Gas is compressed to original state

– Temp rises from TL to TH

– Frictionless piston and quasi-equilibrium – Reversible and adiabatic

Carnot P-V Diagram (Heat Engine)

Reverse Carnot Cycle (Refrigeration)

Carnot Principles

• The efficiency of a irreversible heat engine is always less than a reversible one operating between the same two reservoirs.

• The efficiencies of all reversible heat engines operating between the same two reservoirs are the same.