Work and heat

Work and Heat
Dr. Rohit Singh Lather

Forms of Energy
Energy
Macroscopic Microscopic
Kinetic Potential
Sensible
(translational + rotational + vibrational)
Latent
(inter molecular phase change)
Chemical
(Atomic Bonds)
Atomic
(bonds within nucleolus of atoms)
Summation of all the microscopic energies is called Internal Energy
E= U+KE+PE (kJ)
Low Grade High GradeHeat Work
24/08/16 Dr. Rohit Singh Lather - Engineering Thermodynamics 2

Introduction
• Temperature determines the direction of flow of thermal energy between two
bodies in thermal equilibrium
• Temperature is also a measure of the average kinetic energy of particles in a
substance
• Changes in the state of a system are produced by interactions with the
environment through heat and work
• Heat and work are two different modes of energy transfer
• During these interactions, equilibrium (a static or quasi-static process) is
necessary for the equations that relate system properties to one-another to be
valid
Heat is the random motion of the
particles in the gas, i.e. a
“degraded” from of kinetic energy
• Bodies don't “contain” heat
• Heat is identified as it comes across
system boundaries
• The amount of heat needed to go from
one state to another is path dependent

System
Surroundings
SystemSystem
Surroundings Surroundings
System at higher temperature
looses energy as heat
System and surrounding at
same temperature, no energy
is transferred as heat
System at lower temperature
gains energy as heat
0,0
,
=Δ=Δ
↑Δ↑Δ
ΔΔ
UTif
UTif
TU α
All of the energy inside a system is called INTERNAL ENERGY
When you add HEAT (Q), you are adding energy and the internal energy INCREASES
QReleased = Negative (-) QAbsorbed = Positive (+)

Specific Heat
• Note: It is easy to change the temperature of some things (e.g. air) and hard to change the
temperature of others (e.g. water, block of steel)
• The amount of heat (Q) added into a body of mass m to change its temperature an amount is given
by
Q= m.C.∆T = m.C.(Tf – Ti)
C is called the specific heat and depends on the material
Note: Temperature in either Kelvin or Celsius
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
Δ
=
Ckg
J
Cg
cal
Tm
Q
C oo
The heat capacity C of an object is the proportionality constant between the heat Q
that the object absorbs or loses and the resulting temperature change ΔT of the object
# It is important to distinguish the heat transfer is done with constant volume or constant pressure
The specific heat is different for different processes, particular for gases

Heat of Transformation
When the phase change is between liquid to gas, the heat of transformation is called the
heat of vaporization LV
(# sublimation: transition from solid directly to gas phases)
The amount of energy per unit mass that must be transferred as heat when a sample completely
undergoes a phase change is called the heat of transformation L (or latent heat)
When a sample of mass m completely undergoes a phase change, the total energy transferred is:
When the phase change is between solid to liquid, the heat of transformation is called the
heat of fusion LF
Source: Yunus A. Cengel and Michael A. Boles Thermodynamics: An Engineering Approach, McGraw Hill, 8th Edition

• The amount of energy needed to raise the temperature of a unit of mass of a substance by one
degree is called the specific heat at constant volume Cv for a constant-volume process:
• The amount of energy needed to raise the temperature of a unit of mass of a substance by one
degree is called the specific heat at constant pressure Cp for a constant pressure process:
3-31Heat Capacities at Constant Volume and Constant Pressure
• For ideal gases u, h, Cv, and Cp are functions of temperature alone

Experimental apparatus used by Joule
It has been demonstrated mathematically and experimentally (Joule, 1843) that for an ideal gas the
internal energy is a function of the temperature only. That is, u = u(T)
Water
EvacuatedAir
(high pressure)
Thermometer

• Joule’s reasoned, the internal energy is a function of temperature only and not a function of
pressure or specific volume
• Later Joule’s showed that for gases that deviate significantly from ideal- gas behavior, the
internal energy is not a function of temperature alone
• Using the definition of enthalpy and the equation of state of an ideal gas, we have is also a
function of temperature only h = h(T)
Since u and h depend only on temperature for an ideal gas, the specific heats cv and cp also depend,
at most, on temperature only.
Therefore, at a given temperature, u, h, cv, and cp of an ideal gas have fixed values regard- less of
the specific volume or pressure
Thus, for ideal gases, the partial derivatives in Eqs. 4–19 and 4–20 can be replaced by ordinary
derivatives. Then, the differential changes in the internal energy and enthalpy of an ideal gas can be
expressed as
u = u(T) For ideal gases, u, h, cv, and cp vary with temperature only
du = cv(T) dT

• For ideal gases Cv, and Cp are related by: Cp = Cv + R [kJ / (kg.K)]
• The specific heat ratio 𝛾 is defined as: 𝛾 =
𝑪 𝒑
𝑪 𝒗
• For incompressible substances (liquids and solids), both the constant-pressure and
constant-volume specific heats are identical and denoted by C:
Cp = Cv = C [kJ / (kg.K)]
Cp > Cv In an isobaric process system is heated and work is performed
CV CP
Monoatomic Gases %
&
R
%
&
R
Diatomic Gases %
&
R
%
&
R
Triatomic Gases %
&
R
%
&
R

Heat Transfer Mechanisms
Conduction: (solids--mostly)
Heat transfer without mass transfer
Radiation
Heat transfer through electromagnetic waves
Convection: (liquids/gas)
Heat transfer with mass
transfer due to motion

Conduction
If Q be the energy that is transferred as heat through the
slab, from its hot face to its cold face, in time t, then the
conduction rate Pcond (the amount of energy transferred per
unit time) isTH
Hot
Reservoir
TC
Cold
Reservoir
Q
Slab of face area A &
Thermal conductivity k
Thickness L
We assume steady state
of heat transfer
Here k, called the thermal conductivity, is a constant
that depends on the material of which the slab is made

Convection
• In convection, thermal energy is transferred by bulk motion of materials from regions of high to
low temperatures
• This occurs when in a fluid a large temperature difference is formed within a short vertical
distance (the temperature gradient is large)
• Typically very complicated
• Very efficient way to transfer energy

Radiation
• Everything that has a temperature radiates energy
• Method that energy from sun reaches the earth
• In radiation, an object and its environment can exchange energy as heat via electromagnetic waves
• Energy transferred in this way is called thermal radiation
• The rate Prad at which an object emits energy via electromagnetic radiation depends on the
object’s surface area A and the temperature T of that area in K, and is given by
• Note: if we double the temperature, the power radiated goes up by 24 =16
• If we triple the temperature, the radiated power goes up by 34=81
Stefan–Boltzmann constant
5.6704 x10-8 W/m2 K4
Emissivity
If the rate at which an object absorbs energy via
thermal radiation from its environment is Pabs, then
the object’s net rate Pnet of energy exchange due
to thermal radiation is

Quasi-Static Process
• Arbitrarily slow process such that system always stays stays arbitrarily close to thermodynamic
equilibrium
• Infinite slowness is the characteristics of a quasi-static process
• It is a succession of equilibrium states
• A quasi-static process is also reversible process
Dots indicate
equilibrium states
Pressure
1
2
Volume
Every state passed through by the
system will be an equilibrium state
Such a process is locus of all the
equilibrium points passed through by
the system
System Boundary
Piston
Weight
Final State
Initial State
Multiple
Weights
Final State
Initial State
Piston
dv
dp

Work
• Heat is a way of changing the energy of a system by virtue of a temperature
difference only
• Other means for changing the energy of a system is called work
• We can have push-pull work
- (e.g. in a piston-cylinder, lifting a weight)
- electric and magnetic work (e.g. an electric motor)
- chemical work, surface tension work, elastic work, etc.
• In defining work, we focus on the effects that the system (e.g. an engine) has on
its surroundings
If work is done on the system
the work is negative
(energy added to the system)
Work as being positive when the system
does work on the surroundings
(energy leaves the system)

Pressure Volume Diagrams and Work Done
This area represents the work
done by the gas
(on the surroundings)
when it expands
from state A to state B
Pressure
Volume
Changes that happen during a
thermodynamic process can usefully be
shown on a pV diagram

Work Done by a Gas (Constant Pressure)
Work = force x distance
= force x Δx
= PAΔx (Pressure = F/A so F = PA)
= pΔV (AΔx = ΔV)
Q P
Δx
A
ThermalReservoir
ΔV
Pressure
VolumeV1 V2
PI = PF = P

• The “negative” sign in the equation for WORK is often misunderstood
• Since work done by a gas has a positive volume change we must understand that the gas itself is
USING UP ENERGY or in other words, it is losing energy, thus the negative sign
• When work is done ON a gas the change in volume is negative, this cancels out the negative sign in
the equation, this makes sense as some EXTERNAL agent is ADDING energy to the gas
W = - P ΔV
ΔV = Positive + Work done by System
ΔV = Negative (-) done on system
Work done by System is Negative (-)
Work done on system is Positive (+)

Expansion and Non-Expansion Work
• Electrical work (kJ):
• Boundary work (kJ):
• Gravitational work (kJ):
• Acceleration work (kJ) :
• Shaft work (kJ):
• Spring work (kJ):

POSITIVE WORK
LESS WORK
NEGATIVE WORK
MORE WORK
VolumePressureVolume
Pressure
W > 0
W > 0
Volume
Pressure
1
2
W > 0
Volume
1
2
W < 0
Pressure24/08/16 Dr. Rohit Singh Lather - Engineering Thermodynamics 21

Volume
Pressure
1
2
CYCLIC POSITIVE NET WORK
The work done on a system during a closed cycle can be non-zero
• To go from the state (Vi, Pi) by the path (a) to the state (Vf, Pf) requires a different amount of
work then by path (b).
• To return to the initial point (1) requires the work to be nonzero
Wnet > 0
Volume
Pressure
CONTROL WORK
The work done on a system depends on the path taken in the PV diagram

How do you change Internal Energy (∆U)
Q
Thermal Reservoir
Change in Volume
∆U = Q + W ∆U = Q - W Won the gas = – Wby the gas
Supplying Heat
Work
OR AS
The first law of thermodynamics (closed system) states that the change in internal energy (DU)
is the sum of the work and heat changes: it is applicable to any process that begins and ends
in equilibrium states
All the energies received are turned into the energy of the system: this is a form of the
energy conservation law

• Internal Energy (U) is a state function: a property that depends only on the current
state of the system and is independent of how that state was prepared
• Energy can cross the boundaries of a closed system in the form of heat or work
• If the energy transfer across the boundaries of a closed system is due
to a temperature difference, it is heat; otherwise, it is work

Thermodynamic Processes - Ideal Gas Processes
• States of a thermodynamic system can be changed by interacting with its
surrounding through work and heat. When this change occurs in a system, it is
said that the system is undergoing a process.
• A thermodynamic cycle is a sequence of different processes that begins and ends
at the same thermodynamic state.
• Some sample processes:
− Isothermal Process: Temperature is constant T=C
− Isobaric Process: Pressure is constant, P=C
− Constant Volume Process: Volume is V=C
− Adiabatic Process: No heat transfer, Q=0
− Isentropic Process: entropy is constant, (n = 𝛾), s=C

Isothermal Process
Q = W
W = ∫ 𝑷𝒅𝑽
𝟐
𝟏
W = ∫
𝒎𝑹𝑻
𝑽
𝒅𝑽
𝟐
𝟏
W = mRT∫
𝒅𝑽
𝑽
𝟐
𝟏
Assumptions: Ideal gas
(closed system)
W = mRT In
𝑽 𝟐
𝑽 𝟏
W = mRT In
𝑷 𝟏
𝑷 𝟐
ΔT = 0, then ΔU = 0
ΔU = Q - WWork done by System
ΔU = Q - WWork done by System
Q = WWork done by System
Isotherm
Pressure
1
2
VolumeV1 V2
To keep the temperature constant both the
pressure and volume change to compensate (Volume
goes up, pressure goes down)
“BOYLES’ LAW”
T2 = T1
Q
W
V1
V2
Internal Energy
Does not Change

Reversible process can be reversed by an infinitesimal change in a variable
E.g. reversible, isothermal expansion of an ideal gas
Work done is the area beneath the ideal
gas isotherm lying between the initial and
the final volumes
Pi
Pf
P=nRT/V
Vi Vf
Pressure
Volume
w

Isobaric Process
• In isobaric process P = C , then ∆U = Q – W
𝟐
𝟏
W = P∫ 𝒅𝑽
𝟐
𝟏
W = P (V2 – V1)
Heat is added to the gas which increases the
Internal Energy (U)
∆U = Q - W can be used
since the in this case
Pressure
1
2
VolumeV1 V2
P2 = P1
Q
W = p (V2 – V1)
V1
V2
The path of an isobaric process is a
horizontal line called an isobar
V2 – V1
p
Work is done by the gas as it changes in volume
T2 = T1

Isochoric / Isometric Process
• In isobaric process V = C ∆U = Q – W
W = ∫ 𝑷𝒅𝑽 = 𝟎
𝟐
𝟏
Ideal gas assumption
(closed system)
Q = m.∆U = m∫ 𝑪 𝑽
𝒅𝑻
𝟐
𝟏
No work done
Since, ∆V = 0
∆U = Q – Wby
∆U = Q – 0
∆U = Q
Pressure
1
2
Volume
V1
V2
V2 = V1
Q
V2 = V1 W = 0
T2 > T1

Adiabatic Process
• Adiabatic process Q = 0 ∆U = Q – W
∆U = - W
dW = dU
Ideal gas assumption
(closed system)
dU + PdV = 0
m.CV.dT + (
345
6
) dV = 0
CV.dT + (
45
6
) dV = 0
5&
57
= (
𝑉1
𝑉2
)
(𝛾− 1)
Integrate and R = Cp - CvCv lnT + R lnV = C
(
;<
;=
- 1) InV + In T = C
(𝛾 - 1) In V + In T = C
InV (𝛾- 1) + In T = C
In (T V (𝛾- 1) ) = C
T V (𝛾- 1) = C
T1 V1
(𝛾- 1) = T2 V2
(𝛾- 1)
(infinitesimal increment
of work and energy)
Pressure
1
2
VolumeV1 V2
Q = 0 V1
V2
T1 > T2
P,V, T Change
Adiabat
T1
T2
Wby = - ∆U
Loosing internal energy

5&
57
= (
𝑉1
𝑉2
)
(𝛾− 1)
PV= nRT T = PV/nRT1 V1
(𝛾- 1) = T2 V2
(𝛾- 1)
>767
?4
V1
(𝛾- 1) =
>&6&
?4
V2
(𝛾- 1)
P1V1
𝛾 = P2V2
𝛾
Relation of Temperature with Volume
Relation of Pressure with Volume

Polytropic Process
• ”Polytropic" describes any reversible process on any open or closed system of gas or vapor which
involves both heat and work transfer, such that a specified combination of properties were
maintained constant throughout the process
• The expression relating the properties of the system throughout the process is called
the Polytropic path
• Polytropic Process: its P-V relation can be expressed as
PVn = Constant (c)
Where, n is a constant for a specific process
- Isothermal, T = constant, if the gas is an ideal gas then P.V = R.T = constant, n = 1
- Isobaric, P = constant, n = 0 (for all substances)
- Constant-volume, V = constant, V = constant(P)(1/n), n =∞, (for all substances)
- Adiabatic Process, n = k for an ideal gas

PV Diagram for various Polytropic Processes
P1 V1
𝛾 = P2 V2
𝛾
= PVn
𝟐
𝟏
W = ∫ 𝑷𝑽 𝒏 𝑽⁻ 𝒏 𝒅𝑽
𝟐
𝟏
W = 𝑷𝑽 𝒏
∫ 𝑽⁻ 𝒏 𝒅𝑽
𝟐
𝟏
W =
𝑷𝑽 𝒏
𝟏 B 𝒏
(𝑽 𝟐
𝟏B𝒏 − 𝑽 𝟏
𝟏B𝒏)
W =
𝑷 𝟐 𝑽 𝟐
− 𝑷 𝟏 𝑽 𝟏

𝟏 B 𝒏
Pressure
Volume
n = 0
n = infinity
n > 1
n = 1
n < 1
E
𝑪
𝑽 𝒏
𝟐
𝟏
𝐝𝐕
Polytropic
Adiabatic
Isothermal
Isobaric
Isochoric

In Summary
Process Important Point to Remember Gas Law that identifies it
Isothermal Constant T, dU = 0, Q = W Boyles Law
Isochoric Constant V, W = 0, dU = Q Charles Law
Isobaric Constant P, dU = Q – ( - PdV) Gay – Lussac’s Law
Adiabatic Nothing is Constant , Q = 0, dU = - W Combined Gas Law

Source: http://www.learneasy.info/MDME/MEMmods/MEM23006A/thermo/gases_files/gas_equations.png

Work and heat

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