Design for Manufacture

3. Thermodynamics Thermodynamics

• Thermodynamics – study of heat related matter in motion. • Ma jor devel opments d uri ng 1650 -1850 • Engineering thermodynamics mainly concerned with work produc ing or utili si ng machi nes such as - Engines, - TbiTurbines and - Compressors together w ith th e worki ng sub stances used i n th e machi nes.

• Working substance – fluids: capable of deformation, energy transfer • Air an d s team are common worki ng sub st ance

Design and Manufacture Pressure

F P = A

Force per unit area. Unit: Pascal (Pa) N / m 2

1 Bar =105 Pa

1 standard atmosphere = 1.01325 Bar

1 Bar =14.504 Psi (pound force / square inch, 1N= 0.2248 pound force)

1 Psi= 6894.76 Pa

Design and Manufacture Phase

Nature of substance. Matter can exists in three phases: solid, liquid and gas

Cycle

If a substance undergoes a series of processes and return to its original state, then it is said to have been taken through a cycle.

Design for Manufacture Process

A substance is undergone a process if the state is changed by operation carried out on it

Isothermal process - Constant temperature process

Isobaric process - Constant pressure process

Isometric process or isochoric process - Constant volume process

Adiabatic Process No heat is transferred, if a process happens so quickly that there is no time to transfer heat, or the system is very well insulated from its surroundings.

Polytropic process Occurs with an interchange of both heat and work between the system and its surroundings E.g. Nonadiabatic expansion or compression

Design for Manufacture Energy, Work and Power

Energy - Capacity of doing work

Work - A force is moved through a distance

In a piston, if pressure is constant work done = PA × L = P × AL = P(V2 − V1 ) Nm (Joule)

In variable pressure case

V work done = 2 P dV ∫V 1

P P1

P

P2

V1 V2 V L

Power - Rate of doing work J/s = Watt

Design for Manufacture Work done in polytropic process

workdone

V = 2 PdV ∫V 1 V =C 2 V −n dV ∫V 1

C −n+1 −n+1 = (V −V ) −n+1 2 1

PV −PV = 1 1 2 2 n−1

Design and Manufacture Heat

Tempp()erature t (Celsius) = T-273.15 (()Kelvin)

Q – heat energy joules/kg

SifihtSpecific heat capacit y: heat transfer per unit temperature:

dQ c = dt

Unit: joules/kg K (joules per kg per K)

Calorific value

The heat liberated byyg burning unit mass or volume of a fuel. e.g. petrol: 43MJ/kg

Principle of the thermodynamic engine

Q Q-W Source Engine Sink

W The Conservation of Energy

For a system

Initial Energy + Energy Entering = Final Energy +Energy Leaving

Thermal efficiency

Work done W η = = Heat received Q

Heat Engines An engine in which transfers energy results from difference in temperature. Mechanical Power

Work done Power = Time Taken Unit: J/s= watt

Electrical Power

W = I V

UJ/WUnit: J/s=Watt Laws of Thermodynamics

The zeroth Law

Iffy body A and B are in thermal eq uilibrium, and A and C are in thermal equilibrium, then, B and C must in thermal equilibrium.

The first law

W=Q

Means if some work W is converted to heat Q or some heat Q is converted to work W, W=Q. It does not mean all work can convert to heat in a particular process. The second law

Nature heat transfer will occur down a temperature gradient.

The third law

At the absolute zero of temperature the entropy of a perfect crystal of a substance is zero. Gas laws

Boyle’s law (1662)

For perfect gas

PV=C -constant Temperature remains constant. or

P1V1 = P2V2 - constant T (Isothermal process)

Charle’s Law (work by 1780, Gay-Lussac 1802 published)

V = constant T - constant P (Isobaric process)

Gay-Lussac' sslaw law ( Actually by Guillaume Amontons 1700)

P = constant (Isometric process) T -- constant V Combined gas law (1834 by Clapeyron, 1856 by Kronig, 1857 by Causius) V P Let PV = c , = c and = c 1 T 2 T 3 V P PV PV ⋅ ⋅ = c c c or = c c c T T 1 2 3 T 1 2 3

PV = a (constant) T or

PV P V 1 1 = 2 2 T1 T2

Let mR=a, where m is the mass,

R - specific gas constant (air: R=287 J/kgK)

PV = mR T - characteristic equation of gas (adiabatic with surroundings) Joule’s law

Internal energy of gas is the function of temperature only and independent of changes in volume and pressure.

The specific heat capacity at constant volume cv

U 2 −U1 = mcv ()T2 − T1 (change in internal energy)

The specifi c h eat capacit y at const ant pressure c p

U 2 −U1 + P(V2 −V1) = mc p (T2 − T1 ) Polytropic Process

n PV = C

When n=1, isothermal process;

When n = c p / cv = γ , it is an adiabatic process

From

n n P1V1 = P2V2

n −n −1/ n P1 ⎛V2 ⎞ ⎛ V1 ⎞ V1 ⎛ P1 ⎞ = ⎜ ⎟ = ⎜ ⎟ and =⎜ ⎟ P2 ⎝ V1 ⎠ ⎝V2 ⎠ V2 ⎝ P2 ⎠

From the gas characteristic equation

PV P V 1 1 = 2 2 T1 T2

n n−1 T1 P1V1 ⎛V2 ⎞ V1 ⎛V2 ⎞ = = ⎜ ⎟ = ⎜ ⎟ T2 P2V2 ⎝ V1 ⎠ V2 ⎝ V1 ⎠ and n−1 −1/ n n T1 P1V1 P1 ⎛ P1 ⎞ ⎛ P1 ⎞ = = ⎜ ⎟ = ⎜ ⎟ T2 P2V2 P2 ⎝ P2 ⎠ ⎝ P2 ⎠ i.e.

n−1 T1 ⎛V2 ⎞ = ⎜ ⎟ T2 ⎝ V1 ⎠ n−1 n T1 ⎛ P1 ⎞ = ⎜ ⎟ T2 ⎝ P2 ⎠ Enthalpy

- To describe total energy in gas

H = U + P V

U – internal energy

P – pressure v – volume

Specific Enthalpy h =U/m= u + P v

Design for Manufacture Entropy

T (absolute temperature)

Area = heat transferred

s(entropy) s1 s2

Entropy is a quantity s that associates with the temperature T and heat transfer Qrev in the following way: ΔQ Δs = rev T dQ ds = rev or dQ = Tds T rev where Qrev - reversible heat transfer:

s2 Qrev = T ds ∫s 1 Entropy describes the availability of thermal energy. An isolated system can only change to states of equal or greater entropy.