1. Chapter 11: Energy in Thermal Process
Example homework problems: 11,17,27,38,65
Heat and Internal Energy
Terminology
Internal energy U is the energy associated with microscopic
components of a system – the atoms and molecules of the system.
It includes kinetic and potential energy associated with the random
translational, and vibrational motion of the particles that make up
the system, and any potential energy bonding the particles together.
Heat Q is the transfer of energy between a system and its
environment due to a temperature difference between them.

2. Heat and Internal Energy
Units of heat
Calorie (cal)
The energy necessary to raise the temperature of 1 g of water
from 14.5o to 15.5oC. “Cal” used for energy content in food is kcal.
British thermal unit (Btu)
The energy necessary to raise the temperature of 1 lb of water
from 63o to 64oF.
SI unit : joule (J)
1 cal = J

3. Heat and Internal Energy
Example
Example 11.1 : Working off breakfast
Breakfast : two bowls of cereal and milk, 3.20x102 Cal
Exercise : Do curls with a 25.0-kg barbell to consume all the
calories from the breakfast
Breakfast calories:
Work done by one lifting or lowering barbell:
Number of repetitions n needed:
But see the remark on p.354!

4. Heat and Internal Energy
Specific heat
Definition of specific heat
SI unit : joule per kilo-gram
degree Celsius
J/(kg oC)
DT=Tf-Ti
The energy required to raise the temp.
of kg of water by 3.00oC.

5. Heat and Internal Energy
Specific heat
Example 11.2 : Stressing a strut
A steel strut near a ship’s furnace :
L0=2.00 m, ms=1.57 kg, A=1.00x10-4 m2, Q=2.50x105 J.
(a) Find the change in temp. of the strut.
cs=448 J/(kg oC)
(b) Find the change in length of the strut if it is allowed to expand.
a=11x10-6 oC-1
(c) Find the compressional stress in the strut.
Y=2.00x1011 Pa

6. Calorimetry A system whose energy does not leave out of the system is
Isolated system
A system whose energy does not leave out of the system is
called isolated system.
The principle of energy conservation for an isolated system
requires that the net result of all the energy transfer is zero.
If one part of the system loses energy, another part has to
gain the energy.
Calorimeter and calorimetry
Imagine a vessel made of good insulating material and containing
cold water of known mass and temperature and the temperature of
the water can be measure. Such a system of the vessel and water
is called calorimeter. If the object is heated to a higher temperature
of known value before it is put into the water in the vessel, the specific
heat of the object can be measured by measuring the change in
temperature of the water when the system (the object, vessel, and
water) reaches thermal equilibrium. This measuring process is called
calorimetry.

7. Calorimetry
Calorimeter and calorimetry
When a warm object, put into a calorimeter with cooler water
described in the previous page, becomes cooler while the water
becomes warmer.
Qcold (>0 ) is the heat transferred (energy change) to the cooler
object and Qhot (<0) is the heat transferred (energy change) to the
warmer object.
In general, in an isolated system consisting of n objects :
Tf common to all objects in equilibrium.

8. Calorimetry Example 11.3 : Finding a specific heat
Calorimeter and calorimetry
Example 11.3 : Finding a specific heat
A 125-g block of an unknown substance with a temperature of 90.0oC
is placed in a Styrofoam cup containing kg of water at 20.0oC.
The system reaches an equilibrium temperature of 22.4oC. What is
the specific heat, cx , of the unknown substance if the heat capacity of
the cup is ignored.

9. Calorimetry Example 11.4 : Calculate an equilibrium temperature
Calorimeter and calorimetry
Example 11.4 : Calculate an equilibrium temperature
Suppose kg of water initially at 40.0oC is poured into a kg
glass beaker having a temperature of 25.0oC. A kg block of
aluminum at 37.0oC is placed in the water, and the system is insulated.
Calculate the final equilibrium temperature of the system.

10. Calorimetry Phase change (change of molecular structure)
Latent heat and phase change
Phase change (change of molecular structure)
- Phases of material : solid, liquid, gas
- A change of phase : phase transition
- For any given pressure a phase change takes place at a
definite temperature, usually accompanied by absorption
or emission of heat and a change of volume and density
Heated added and phase changes of water

11. Calorimetry Latent heat
Latent heat and phase change
Latent heat
- To change structure of material, change in energy required.
When a substance goes under phase transition, all the heat
transferred is used to change the phase.
L : latent heat (J/kg) , m : mass (kg)
+(-) when energy is absorbed (removed).
Heated added and phase changes of water

12. Calorimetry Latent heat
Latent heat and phase change
Latent heat
The latent heat of fusion Lf is used when a phase change occurs
during melting or freezing.
The latent heat of vaporization Lv is used when a phase change
occurs during boiling or condensing.

13. Calorimetry
Latent heat and phase change
Water
Consider an addition of energy to a 1.00-g cube of ice at -30.0oC in
a container held at constant pressure. Suppose this input energy
turns ice to steam (water vapor) at 120.0oC. A: B: C: D: E:

14. Calorimetry Example 11.5 : Boiling liquid helium
Latent heat and phase change
Example 11.5 : Boiling liquid helium
Liquid helium has a very low boiling point, 4.2 K, as well as a low latent
heat of vaporization, 2.09x104 J/kg. If energy is transferred to a container
of liquid helium at the boiling point from an immersed electric heater at
a rate of 10.0 W, how long does it take to boil away 2.00 kg of the liquid?

15. Calorimetry Example 11.6 : Ice water
Latent heat and phase change
Example 11.6 : Ice water
6.00 kg of ice at -5.00oC is added to a cooler holding 30 liters of water
at 20.0oC. What temperature of the water when it comes to equilibrium?
Q m(kg) c(J/(kgoC)) L (J/kg) Tf Ti Exp.
Qice mcDT
Qmelt x mLf
Qice-water T mcDT
Qwater T mcDT

16. Calorimetry Example 11.7 : Ice water
Latent heat and phase change
Example 11.7 : Ice water
A 5.00-kg block of ice at 0oC is added to an insulated container partially
filled with 10.0 kg of water at 15.0oC.
(a) Find the final temperature (neglect the heat capacity of the container.)
The amount of energy needed to completely melt the ice:
The maximum energy that can be lost by the initial mass of liquid water
without freezing it :
Since this is less than half the energy needed to melt all the ice, so the
final state of the system is a mixture of water and ice at the freezing point.
(b) Find the mass of the ice melted.

17. Energy Transfer Thermal conduction Convection Radiation
Mechanism of heat transfer
Thermal conduction
Convection
Radiation
Thermal conduction
One form of heat transfer when there is temperature difference is
thermal conduction.
This process is caused by an exchange of kinetic energy between
microscopic particles such as molecules, atoms, and electrons etc.
In the process, less energetic particles gain energy as they collide
with more energetic particles.
The rate of energy transfer P=Q/Dt is
proportional to cross-sectional area A,
the difference in temperature DT=Th-Tc>0,
and inversely proportional to the thickness
of the slab.

18. Energy Transfer
Thermal conduction
Consider a substance is in the shape of a long, uniform rod of length
L and assume that the rod is insulated so that thermal energy does not
escape from the surface.
k : proportionality constant
thermal conductivity
[J/(s m oC)]
Th : higher temperature (oC)
Tc : lower temperature (oC)
A : area (m2)
L : length (m)
Q : heat transferred (J)
Dt : time interval (s)

19. Energy Transfer Thermal conductivities
Thermal conduction
Thermal conductivities
Example 11.9 : Energy transfer through a concrete
wall
Find the energy transferred in 1.00 h by conduction
through a concrete wall 2.0 m high, 3.65 m long,
and 0.20 m thick if one side of the wall is held at
20oC and the other at 5oC.

20. Energy Transfer Example : Two rods cases k1,L,,A1 k1,L1 k2,L2 Tm
Thermal conduction
Example : Two rods cases
k1,L,,A1
k1,L1
k2,L2 Tm
k2,L,,A2

21. Energy Transfer Thermal conduction through multiple layers L1 L2 L3 k1
Tc1
Tc2
Tc2

22. Energy Transfer Example 11.11 : Staying warm in the arctic
Thermal conduction
Example : Staying warm in the arctic
An arctic explore builds a wooden shelter out of wooden planks that
are 1.0 cm thick. To improve the insulation, he covers the shelter with
a layer of ice 3.2 cm thick.
(a) Compute the R factors for the wooden planks and the ice.
(b) Find the rate of heat loss.
(c) Find the temperature in between the ice and the wood.

23. Energy Transfer
Convection
The transfer of energy by the movement of a substance is called
convection.

24. Heat transfer by radiation
Energy Transfer
Radiation
All objects radiate energy because of microscopic movements
(accelerations) of charges, which increase with temperature.
Heat current in radiation
e : emissivity that depends on nature of surface
T in K
A :area
s= (40) x 10-8 W/(m2 K4) :Stefan-Boltzman const.
If an object is at temperature T and its surroundings are at
temperature T0, the net flow of heat radiation between the object and its surroundings is
Heat transfer by radiation

25. Energy Transfer Example 11.12 : Polar bear club
Radiation
Example : Polar bear club
A member of the Polar Bear Club, dressed only in bathing trunks
of negligible size, prepares to plunge into the Baltic Sea from the
in St. Petersburg, Russia. The air is calm, with a temperature of
5oC. If the swimmer’s surface body temperature is 25oC, compute
the net rate of energy loss from his skin due to radiation. How much
energy is lost in 10.0 min? Assume his emissivity is and his
surface area is 1.50 m2.