Physics - Heat and Thermodynamics - Basics

Heat and Thermodynamics - Transmission of Heat
Ms Dhivya R
Assistant Professor
Department of Physics
Sri Ramakrishna College of Arts and Science
Coimbatore - 641 006
Tamil Nadu, India
1

Heat
Heat transfer is a process by which internal energy from one
substance transfers to another substance.
Thermodynamics is the study of heat transfer and the
changes that result from it.
An understanding of heat transfer is crucial to analyzing
a thermodynamic process, such as those that take place
in heat engines and heat pumps.
 Conduction
 Convection
 Radiation
2

Conduction
 The process in which heat is transmitted from one point to
the other through the substance without the actual
motion of the particles.
 The process of conduction is prominent in the case of
solids.
3

Convection
 The process in which heat is transmitted from one place to
the other by the actual movement of the heated particles.
 The process of convection is prominent in the case of
liquids and gases.
4

Radiation
 The process in which heat is transmitted from one place to
the other directly without the necessity of the intervening
medium.
 Heat radiations can pass through vacuum.
 These properties are similar to that of light radiations.
5

Heat
6

Coefficient of thermal
conductivity
Consider a cube of side = ‘x’ cm & Area of each face = A sq.cm
Temperature of opposite face = 𝜃1 and 𝜃2
Quantity of heat conducted across the two opposite faces
Q α A
Q α 𝜃2 - 𝜃1
Q α t
Q α 1/x
Q α
𝐴 𝜃2 − 𝜃1 𝑡
𝑥
Q =
𝐾𝐴 𝜃2 − 𝜃1 𝑡
𝑥
K = coefficient of thermal conductivity
If A=1 sq.cm 𝜃2 − 𝜃1 = 1oC t = 1, x= 1 cm
Then Q=K
7

conductivity
Definition: The coefficient of thermal conductivity is defined
as the amount of heat flowing in one second across the
opposite faces of a cube of side one cm maintained at a
different of temperature of 10C.
Temperature gradient : The quantity
𝜃2 − 𝜃1
𝑥
represents the
rate of fall of temperature with respect to distance. The
quantity
𝑑𝜃
𝑑𝑥
represents the rate of change of temperature
with respect to the distance. As temperature decreases with
increase in distance from the hot end, the quantity
𝑑𝜃
𝑑𝑥
is
negative and is called the temperature gradient.
8

conductivity
Dimensions of K
K = -Q/A
𝑑𝜃
𝑑𝑥
𝑡
[Q] = [ML2T-2 ], [dx] = [L], [A] = [L2], [dθ] = [θ], [t]= [T]
Therefore
[K] = [MLT-3θ-1]
9

Rectilinear flow of heat along a
bar
Consider a bar of uniform cross
section which is heated in one end.
Consider two planes P1 and P2
perpendicular to the length of the
bar at distance x and x+δx from the
hot end.
The temperature gradient of the
plane P1 =
𝑑𝜃
𝑑𝑥
Excess temperature at P2 =𝜃+
𝑑𝜃
𝑑𝑥
δX
The temperature gradient at P2 =
𝑑 (𝜃+ 𝑑𝜃
𝑑𝑥
δX)
𝑑𝑥
10

bar
Heat flowing through P1in one second
Q1= - KA
𝑑𝜃
𝑑𝑥
Heat flowing through P2 in one second
Q1= - KA
𝑑
𝑑𝑥
(𝜃+
𝑑𝜃
𝑑𝑥
δX)
Heat gained per second by the rod between the plates P1and
P2
Q = Q1-Q2
Q = - KA
𝑑𝜃
𝑑𝑥
+ KA
𝑑
𝑑𝑥
(𝜃+
𝑑𝜃
𝑑𝑥
δX)
Q = KA
𝑑2
𝜃
𝑑𝑥2δX
11

bar
Before the steady state is reached:
The quantity of heat Q is used in two ways before the steady
state is reached.
The heat is used to raise the temperature of the rod
The loss due to radiation.
Let the rate of rise of temperature of the bar be
𝑑𝜃
𝑑𝑥
12

bar
The heat used per second to raise the temperature of the rod
= mass x specific heat x
𝑑𝜃
𝑑𝑥
=(A x δx) ρ x S
𝑑𝜃
𝑑𝑥
A = area of cross section; S = specific heat; Ρ = density of the
material; The heat loss per second due to radiation = Ep δx 𝜃
E = Emissive power of the surface; p = perimeter
𝜃 = average excess of temperature of the bar between the
planes P1 and P2
13

bar
Q =(A x δx) ρ x S
𝑑𝜃
𝑑𝑥
+ Ep δx 𝜃
Substituting the value of Q in above equation
Q = KA
𝑑2
𝜃
𝑑𝑥2δX = (A x δx) ρ x S
𝑑𝜃
𝑑𝑥
+ Ep δx 𝜃
𝑑2
𝜃
𝑑𝑥2 =
𝜌𝑆
𝐾
.
𝑑𝜃
𝑑𝑡
+
𝐸𝑝
𝐾𝐴
θ
This is the general equation that represents the rectilinear
flow of heat along a bar of uniform area of cross section and
is known as Fourier’s differential equation
14

Periodic flow of heat
Metallic bar is alternately heated and cooled (i.e) heat is
supplied periodically (and not continuously).
It is observed that the temperature at different points in the
bar also varies periodically.
Principle:
Whenever the end is heated, the heat waves flow
outward from it and when it is cooled, the heat waves travel
towards it and thus two waves are set up in the rod travelling
in opposite directions.
15

Periodic flow of heat
Assuming that there is no loss due to radiation as it is well insulated, the
problem becomes simpler. It is just like the propagation of periodic heat
only in one direction. Let the periodic variation of temperature be
represented by
θ= θo cos ω t
Where θo = amplitude
Ω = angular frequency
The variation can be represented by
sinusoidal curve of damped nature
16

Thermal conductivity measurement
(angstrom’s method)
To determine the conductivity of a metal bar by using the
method of periodic flow.
Long metal bar- enclosed one end of it in a chamber through
which steam and cold water at known temperature could be
alternately passed.
The end of the bar is heated for 12 mins and cooled for 12
mins by passing cooled water. The periodic time of heat flow
is T = 24 mins.
Until steady state is reached.
17

Thermal conductivity measurement
(angstrom’s method)
Then the maximum temperature at two consecutive points is
noted.
The distance between these two points is measured by using
thermo-couple.
Knowing λ, T, the value K the thermal conductivity can be
determined by using the formula
K=
𝜆2
𝜌𝑆
4𝜋𝑇
18

Propagation of heat waves in the
Earth’s Crust
Dirunal Wave – The periodic heating and cooling as a result a
heat or temperature wave with a period of 24 hrs is
propagated into the interior of the earth.
Annual Wave – Heat wave travelling into the interior of
earth for the period of 1 year.
19

Searle’s method
XY –Rod (thermal conductivity)
The end X is enclosed in a steam jacket
θ1 θ2 θ3 θ4 – steady state temperature
20

Searle’s method
Quantity of a heat flow from the section at P to Q in one
second =
𝐾𝐴 𝜃1 − 𝜃2 𝑋 1
𝑑
---------------------(i)
The amount of heat gained by water in one second =
𝑚 𝜃4 − 𝜃3
𝑡
--------------------(ii)
Equating (i) and (ii)
𝐾𝐴 𝜃1 − 𝜃2 𝑋 1
𝑑
=
𝑚 𝜃4 − 𝜃3
𝑡
K =
𝑚𝑑 𝜃4 − 𝜃3
𝐴𝑡 𝜃1 − 𝜃2
21

Lee’s method for metals
Low temperature
C- copper Frame, H1- Heating Coil,
AB- specimen rod (10 cm long, 0.5 cm
diameter)
T1, T2 - platinum thermometers,
F – Dewar flask
22

23

Correction
24

Forbes method to find K
Used to find the absolute conductivity of different metals
25

26

Static Experiment:
27

Dynamic Experiment:
28

29
Advantage:
• Absolute conductivity of the
material of the rod can be
determined
Disadvantages:
• Tedious
• S not constant at all temps
• Distribution of heat not same in two
experiments
• Hence not accurate

Spherical Shell method to find K
 Radial flow of heat
 In this method heat flows from the inner side towards the
other side along the radius of the shell.
 This method is useful in determining
the thermal conductivity of bad conductors
taken in the powder form.
30
r1
r2
A
θ1
θ
θ2
B
dr
Θ+dθ

Spherical Shell method to find K
 𝑄 = −𝐾𝐴
𝑑𝜃
𝑑𝑟
 𝐴 = 4𝜋𝑟2
 𝑄 = −𝐾. 4𝜋𝑟2.
𝑑𝜃
𝑑𝑟

𝑑𝑟
𝑟2 = −
4𝜋𝐾
𝑄
. ⅆ𝜃
31
Integrating

𝑟1
𝑟2
ⅆ𝑟
𝑟2 = −
4𝜋𝐾
𝑄 𝜃1
𝜃2
ⅆ𝜃

1
𝑟1
−
1
𝑟2
=
4𝜋𝐾 𝜃1−𝜃2
𝑄
 K =
𝑟2−𝑟1 𝑄
4𝜋𝑟1
𝑟2
𝜃1−𝜃2

Cylindrical Flow of Heat
32

33

34

35

Practical Applications of
Conduction
1. Heat conduction is applied in cooking with metal pot e.g.
Aluminum pots.
2. Ironing of clothes with pressing iron.
3. Welding of two iron metals together.
4. The handles of the cooking utensils are made of materials
like plastic and sometimes wood which cannot conduct
heat when carried by the cook.
36

Conduction
 Ice box has a double wall, made of tin or iron. The space
between the two walls is filed with cork or felt which are
poor conductors of heat. They prevent the flow of outside
heat into the box, thus keeping the ice from melting.
 Woolen clothes have fine pores filled with air. Air and wool
are bad conductors of heat. Thus, the heat from the body
does not flow out to the atmosphere. Thus, the woolen
clothes’ keep the body warm in winter.
 In cold countries windows are provided with double doors.
The air in the space between the two doors forms a non
conducting layer and so heat cannot flow out from inside
the room.
37

Conduction
 In hot countries as well, the windows are made with
double doors. Heat can not flow in from outside because
of the presence of air between the two doors.
 When a stopper, fitted tightly to the bottle is to be
removed, the neck of the bottle is gently heated. It
expands slightly on heating. Since glass is a bad conductor
of heat, the heat does not reach the stopper. Thus, it can
be removed easily.
38

Conduction
 Davy’s Safety Lamp: It is one of the most
important applications of conduction of
heat.https://www.youtube.com/watch?v=kpru-
fEbUIE
 The principle of Davy’s safety lamp can be
understood from a simple example in
which a wire gauze is placed over a
Bunsen burner.
 The gas coming from the burner is lit
above the wire gauze.
 A flame appears at the top surface of the
wire gauze.
39

Conduction
 The gas coming out from the burner below the wire gauze does not
get sufficient heat for ignition.
 The reason is that the wire gauze conducts away the heat of the flame
above it and so the temperature at the lower surface of the gauze
does not reach the ignition point.
 In Davy’s safety lamp, a cylindrical metal gauze of high thermal
conductivity surround the flame.
 When this lamp is taken inside a mine, the explosive gases present in
the mine are not ignited because the wire gauze in the form a cylinder
conducts away the heat of the flame of the lamp.
 The result is that the temperature outside the gauze remains below
the ignition point of the gases. In absence of the wire gauze the gases
outside can explode.
40

Conduction
41

Physics - Heat and Thermodynamics - Basics

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