1. Introduction to thermodynamics
Prof. Marlon Flores Sacedon
Department of Mathematics and Physics
College of Arts and Sciences
Visayas State University, Visca
Baybay City, Leyte, Phiippines

2. What is Thermodynamics?
Thermodynamics is a study of energy transformations involving heat, mechanical work, and other aspects of energy and how these transformations relate to the properties of matter.

3. Temperature and Heat
Temperature is rooted in qualitative ideas of “hot” and “cold” based on our sense of touch cold.
A body that feels hot usually has a higher temperature than a similar body that feels cold.

4. Temperature and Heat
System A
System B
System C
Insulator
Conductor
System A
System B
System C
Conductor
Insulator
System A
System B
System A
System B
System C
(b) …then A and B are in thermal equilibrium with each other.
(a) If system A and B are each in thermal equilibrium with system C…
If C is initially in thermal equilibrium with both A and B, then A and B are also in thermal equilibrium with each other. This result is called the Zeroth Law of thermodynamics
Zeroth Law of Thermodynamics
Two system are in thermal equilibrium if and only if they have the same temperature.

5. Temperature scale Celsius Fahrenheit Kelvin Rankine
Units of Temperature
Celsius
Fahrenheit
Kelvin
Rankine

6. Temperature scale Temperature Scale At freezing Point of water
Celsius and Fahrenheit relationship
Temperature Scale
At freezing Point of water
At boiling point of water
Celsius , Tc
0 oC
100 oC
Fahrenheit, TF
32 oF
212 oF
𝒎= 𝒓𝒊𝒔𝒆 𝒓𝒖𝒏
= 𝟏𝟖𝟎 𝒐 𝑭 𝟏𝟎𝟎 𝒐 𝑪
= 𝟗 𝒐 𝑭 𝟓 𝒐 𝑪 TC TF
212 oF
100 oC
Linear function 𝒚=𝒎𝒙+𝒃
𝑻 𝑭 = 𝟗 𝒐 𝑭 𝟓 𝒐 𝑪 𝑻 𝑪 +𝟑𝟐 𝒐 𝑭
𝟏𝟖𝟎 𝒐 𝑭
32 oF
𝑻 𝑭 = 𝟗 𝟓 𝑻 𝑪 +𝟑𝟐
𝟏𝟎𝟎 𝒐 𝑪
𝑻 𝑪 = 𝟓 𝟗 𝑻 𝑭 −𝟑𝟐

7. Temperature scale
Kelvin scale
The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics.

8. Temperature scale 𝑻 𝑲 = 𝑻 𝑪 +𝟐𝟕𝟑.𝟏𝟓 Kelvin scale 𝑷 𝑻 𝒐 𝑪 𝟎 𝟏𝟎𝟎 𝟐𝟎𝟎
𝑻 𝒐 𝑪 𝟎
𝟏𝟎𝟎
𝟐𝟎𝟎
−𝟏𝟎𝟎
−𝟐𝟎𝟎
Gas Thermometer
𝟐𝟕𝟑.𝟏𝟓𝑲
−𝟐𝟕𝟑.𝟏𝟓 𝒐 𝑪
𝑻 𝑲
𝟏𝟎𝟎
𝟐𝟎𝟎
𝟑𝟎𝟎
𝟒𝟎𝟎
5𝟎𝟎 𝟎
𝟎𝑲=−𝟐𝟕𝟑.𝟏𝟓 𝒐 𝑪
𝟎 𝒐 𝑪 =𝟐𝟕𝟑.𝟏𝟓𝑲
= 𝟓 𝟗 𝑻 𝑭 −𝟑𝟐 +𝟐𝟕𝟑.𝟏𝟓
𝑻 𝑲 = 𝑻 𝑪 +𝟐𝟕𝟑.𝟏𝟓

9. Temperature scale Instantaneous Temperature, (𝑇) Degree celsius, (𝑜𝐶)
Degree Fahrenheit (𝑜𝐹)
∆𝑻= 𝑻 𝒇𝒊𝒏𝒂𝒍 − 𝑻 𝒊𝒏𝒊𝒕𝒊𝒂𝒍
Change in Temperature, (∆T)
Degree celsius, ( 𝑪 𝒐 )
Degree Fahrenheit ( 𝑭 𝒐 )
Kelvin (𝐾)
𝟏𝑪 𝒐 =𝟏𝑲
𝟏𝑲= 𝟗 𝟓 𝑭 𝒐
Suppose:
𝑻 𝟏 =𝟑𝟎 𝒐 𝑪
𝑻 𝟐 =𝟖𝟎 𝒐 𝑪
Change in Temperature:
∆𝑻= 𝑻 𝟐 − 𝑻 𝟏 =𝟖𝟎 𝒐 𝑪 −𝟑𝟎 𝒐 𝑪 =𝟓𝟎 𝑪 𝒐 =𝟓𝟎𝑲

10. Summary of important formulas
𝑻 𝑭 = 𝟗 𝟓 𝑻 𝑪 +𝟑𝟐
Degree Fahrenheit to Degree Celsius
𝑻 𝑪 = 𝟓 𝟗 𝑻 𝑭 −𝟑𝟐
Degree Celsius to Degree Fahrenheit
𝑻 𝑲 = 𝑻 𝑪 +𝟐𝟕𝟑.𝟏𝟓
Kelvin to Degree Celsius
𝟏𝑪 𝒐 =𝟏𝑲
One Celsius degree is equal to one Kelvin
𝟏𝑲= 𝟗 𝟓 𝑭 𝒐
One Kelvin is equal to 9/5 of Fahrenheit degree

11. Problems
1. Convert the following Celsius temperatures to Fahrenheit: (a) −62.8 𝑜 𝐶 , the lowest temperature ever recorded in North America; (b) 𝑜 𝐶 , the highest temperature ever recorded in the United States; (c) 𝑜 𝐶 , the world’s highest average annual temperature.
a) -81oF, b) 134.1oF, c) 88oF
2. (a) You feel sick and are told that you have a temperature of 𝒐 𝑪 . What is your temperature in 𝒐 𝑭 ? Should you be concerned? (b) The morning weather report in Sydney gives a current temperature of 12 𝒐 𝑪 . What is this temperature in 𝒐 𝑭 ?
a) 104.4oF;yes, b) 54oF
3. Convert the following Kelvin temperature to the Celsius and Fahrenheit scales; (a) the midday temperature at the surface of the moon (400 𝐾); (b) the temperature at the tops of the clouds in the atmosphere of Saturn (95 𝐾); (c) the temperature at the center of the sun (1.55𝑥 10 7 𝐾)

12. These are examples of Thermal Expansion
Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a change in temperature, through heat transfer.
Most materials expand when their temperature increase.
The decks of bridges need special joints and supports to allow for expansion.
A completely filled and tightly capped bottle of water cracks when it is heated
You can loosen a metal jar lid by running hot water over it. .
These are examples of Thermal Expansion

13. Two Kinds of Thermal Expansion Linear Expansion Volume Expansion

14. Thermal Expansion

15. Thermal Expansion

16. Volume Expansion
Linear Expansion T1 Lo T2
T2>T1
MFS

17. MFS Volume Expansion Linear Expansion T1 Lo L T2 @ T2 T2>T1T1 T1 Lo L T2
@ T2
T2>T1
T2>T1
Where: = coef. of linear expansion (1/K)
L = change in length (m)
L & Lo = final & initial length (m)
T2&T1= final & initial temperature (oC)
Where: = coef. of volume expansion (1/K)
V = change in volume (m3)
V & Vo = final & initial volume (m3)
T2&T1= final & initial temperature (oC)
MFS

18. MFS Coefficients of Linear Expansion Coefficients of Volume Expansion
Material
[K-1 or (Co)-1]
Aluminum
2.4x10-5
Brass
2.0x10-5
Copper
1.7x10-5
Glass
x10-5
Invar
0.09x10-5
Quartz
0.04x10-5
Steel
1.2x10-5
Material
[K-1 or (Co)-1]
Aluminum
7.2x10-5
Brass
6.0x10-5
Copper
Glass
x10-5
Invar
0.27x10-5
Quartz
0.12x10-5
Steel
3.6x10-5
Ethanol
75x10-5
Carbon Disulfide
115x10-5
Glycerine
49x10-5
Mercury
18x10-5
MFS

19. Relationship between coefficient of volume expansion & coefficient of linear expansion
Recall:

20. MFS Coefficients of Linear Expansion Coefficients of Volume Expansion
Material
[K-1 or (Co)-1]
Aluminum
2.4x10-5
Brass
2.0x10-5
Copper
1.7x10-5
Glass
x10-5
Invar
0.09x10-5
Quartz
0.04x10-5
Steel
1.2x10-5
Material
[K-1 or (Co)-1]
Aluminum
7.2x10-5
Brass
6.0x10-5
Copper
Glass
x10-5
Invar
0.27x10-5
Quartz
0.12x10-5
Steel
3.6x10-5
Ethanol
75x10-5
Carbon Disulfide
115x10-5
Glycerine
49x10-5
Mercury
18x10-5
Relationship between coefficient of volume expansion & coefficient of linear expansion
MFS

21. Example 1: A surveyor uses a steel measuring tape that is exactly 50
Example 1: A surveyor uses a steel measuring tape that is exactly m long at a temperature of 20 oC. What is its length on a hot summer day when the temperature is 35 oC? Lo
Solution
50 m
Temperature of 20oC
L = ?
Temperature of 35oC
From table, the coefficient of linear expansion
From the formula:
MFS
Ans
Transforming
= m

22. Example 2: A glass flask with volume 200 cm3 is filled to the brim with mercury at 20 oC. How much mercury overflows when the temperature of the system is raised to 100 oC? The coefficient of linear expansion of the glass is 0.40x10-5 K-1.
Solution
Mercury overflows ( Vover)
Mercury, expanded volume( VHg)
Glass flask, expanded volume ( Vglass)
Mercury column
Glass flask
From table:
Glass flask filled w/ mercury
@ T1=20oC
@ T2=100oC
Answer: ∆ 𝑽 𝒐𝒗𝒆𝒓 =𝟐.𝟕 𝒄𝒎 𝟑

23. Seat Work1: The Humber Bridge in England has the world’s longest single span, 1410m in length. Calculate the change in length of steel deck of the span when the temperature increases from -5.0oC to 18.0oC.
Answer: 0.39 m
Seat Work2: A metal rod is cm long at 20.0oC and cm long at 45.0oC. Calculate the average coefficient of linear expansion of the rod for this temperature range.
Answer: 2.3x10-5 (Co)-1
Seat Work3: A glass flask whose volume is cm3 at 0.0oC is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0oC, 8.95 cm3 of mercury overflow. If the coefficient of volume expansion of mercury is 18.0x10-5 K-1, compute the coefficient of volume expansion of the glass.
Answer: 1.7x10-5 (Co)-1

24. Assignment
1) A Pendulum shaft of a clock is made of brass. What is the fractional change in length of the shaft when it is cooled from 19.50oC to 5.00oC?
Answer: -2.9x10-4
2) An underground tank with a capacity of 1700L (1.70m3) is filled with ethanol that has an initial temperature of 19.0oC. After the ethanol has cooled off to the temperature of the tank and ground, which is 10.0oC, how much air space will there be above the ethanol in the tank? (Assume that the volume of the tank doesn’t change.)
Answer: 2.3x10-5 (Co)-1
3) A metal rod that is 30.0 cm long expands by cm when its temperature is raised from 0oC to 100oC. A rod of a different metal and of the same length expands by cm for the same rise in temperature. A third rod, also 30.0 cm long is made up of pieces of each of the above metals placed end-to-end and expands cm between 0oC and 100oC. Find the length of each portion of the composite bar.
Answer: 23.0cm, 7.0cm

25. Prof. Marlon Flores Sacedon
Heat Transfer
Prof. Marlon Flores Sacedon
Department of Mathematics and Physics
College of Arts and Sciences
Visayas State University, Visca
Baybay City, Leyte, Phiippines

26. First long exam Date: Aug 23, 2017 Time: 5:00-7:00 PM Venue: EB-105
Coverage: from start to heat transfer
No. of Items: 60 pts.
Bring the following: Calculator, 5 sheets of yellow, ballpen, etc.

27. How do we describe the difference between these two materials?
Heat Transfer
conductor
insulator
Talking about conductors and insulators, materials that permit or prevent heat transfer between bodies.
In the kitchen you use a metal or glass pot for good heat transfer from the stove to whatever you’re cooking, but your refrigerator is insulated with a material that prevents heat from flowing into the food inside the refrigerator.
How do we describe the difference between these two materials?
The answer is heat transfer.

28. Heat Transfer
Heat transfer is the exchange of thermal energy between physical systems. The rate of heat transfer is dependent on the temperatures of the systems and the properties of the intervening medium through which the heat is transferred.

29. Three Mechanisms of Heat Transfer
Conduction
Heat transfer occurs within a body or between two bodies in contact.
Conduction is the process by which heat energy is transmitted through collisions between neighboring molecules.

30. Three Mechanisms of Heat Transfer
ConVECtion
is the transfer of heat from one place to another by the movement of fluids. Convection is usually the dominant form of heat transfer(convection) in liquids and gases.

31. Three Mechanisms of Heat Transfer
RADIAtion
Heat transfer by electromagnetic radiation, such as sunshine, with no need for matter to be present in the space between bodies.

35. Conduction Steady-state heat flow due to conduction in a uniform rod.
Where:
H = heat current (W or watt)
k = thermal conductivity (W/m.K)
TH & Tc = hot and cold temperature (oC)
A = area of conductor (m2)
L = length of conductor (m)
(TH - Tc)/L = temperature gradient (K/m)

37. Example 1: A Styrofoam cooler (Right Figure) has total wall area (including the lid) of 0.80 m2 and wall thickness 2.0 cm. It is filled with ice, water, and cans of Omni-Cola, all at 0oC. What is the rate of heat flow into the cooler if the temperature of the outside wall is 30oC? How much ice melts in 3 hours?
𝐻= 0.027𝑊/𝑚∙𝐾 𝑚 𝒐 𝑪 −𝟎 𝒐 𝑪 𝑚
=32.4 𝑊=32.4 𝐽/𝑠
𝑄=𝑚 𝐿 𝑓
𝑚= 𝑄 𝐿 𝑓
= 𝐽/𝑠 10,800 𝑠 3.34𝑥 𝐽/𝑘𝑔
=1.0 𝑘𝑔

38. Example 2. A steel bar 10.0 cm long is welded end to end to a copper bar 20.0 cm long. Each bar has a square cross section, 2.00 cm on a side. The free end of the steel bar is kept at 100oC by placing it in contact with steam, and the free end of the copper bar is kept at 0oC by placing it in contact with ice. Both bars are perfectly insulated on their sides. Find the steady-state temperature at the junction of the two bars and the total rate of heat flow through the bars.

39. Assignment

40. Assignment

41. Assignment

42. Answers to odd numbers

43. Equation of State

44. Learning Goal:
How to relate the pressure, volume, and temperature of a gas.

45. What are the physical quantities present on the gas inside a container?
Number of moles, n
Volume, V
Pressure, p
Temperature, T
These variables describe the state of the material and are called state variables.
The relationship among p, V, T, and m (or n) is simple enough that we can express it as an equation called the Equation of State.

46. Measurements of the behavior of various gases lead to four conclusions:
1. The volume V is proportional to the number of moles n. If we double the number of moles, keeping pressure and temperature constant, the volume doubles.
(Avogadro’s Law, constant p & T )
2. The volume varies inversely with the absolute pressure p. If we double the pressure while holding the temperature T and number of moles n constant, the gas compresses to one-half of its initial volume. In other words, pV=constant when n and T are constant.
(Boyle’s Law, constant n & T)
𝒑𝑽=𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
3. The volume is proportional to the absolute temperature, keeping the pressure and number of moles constant,
(Charle’s Law, constant n & p)
4. The pressure is proportional to the absolute temperature. If we double the absolute temperature, keeping the volume and number of moles constant, the pressure doubles. In other words, p = (constant) T when n and V are constant.
(Gay Lussac’s Law, constant n & V

47. Measurements of the behavior of various gases lead to three conclusions:
(Ideal-gas equation)
Where:
p = pressure (Pa)
V = volume (m3)
n = number of moles (mol)
T = absolute temperature (K)
R = ideal gas constant
R= J/mol.K
R= L.atm/mol.K
Note: 1 atm = 1.013x105 Pa
1 m3 = 1,000 L
Where:
M = molar mass (kg/mol)
m = mass (kg)

48. Example 1. What is the volume of a container that holds exactly 1 mole of an ideal gas at standard temperature and pressure (STP), defined as T = 0 oC = K and p = 1atm = 1.013x105 Pa?
From Equation of state for ideal gas:
= 1𝑚𝑜𝑙 𝐽 𝑚𝑜𝑙∙𝐾 𝐾 𝑥 10 5 𝑃𝑎
V= 𝑛𝑅𝑇 𝑝
= 𝑚 3 =22.4 𝐿

49. Problems
1. A 20.0-L tank contains 4.86x10-4kg of helium at 18.0oC . The molar mass of helium is 4.00g/mol (a) How many moles of helium are in the tank? (b) What is the pressure in the tank, in pascals and in atmospheres?
0.122 mol
14.7x103 Pa, 0.145a tm
2. Helium gas with a volume of 3.20 L, under a pressure of atm and at 41.0C, is warmed until both pressure and volume are doubled. (a) What is the final temperature? (b) How many grams of helium are there? The molar mass of helium is 4.00 g/mol.
3. A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.11 m3 of air at a pressure of atm. The piston is slowly pulled out until the volume of the gas is increased to 0.39m3. If the temperature remains constant, what is the final value of the pressure?
Ans: atm

50. Problems
4. A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains m3 of air at a pressure of atm. The piston is slowly pulled out until the volume of the gas is increased to m3. If the temperature remains constant, what is the final value of the pressure?
5 . A 3.00-L tank contains air at 3.00 atm and 20.oC. The tank is sealed and cooled until the pressure is 1.00 atm. (a) What is the temperature then in degrees Celsius? Assume that the volume of the tank is constant. (b) If the temperature is kept at the value found in part (a) and the gas is compressed, what is the volume when the pressure again becomes 3.00 atm?
6 A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm3 of air at atmospheric pressure (1.01x105 Pa) and a temperature of 27.oC. At the end of the stroke, the air has been compressed to a volume of 46.2 cm3 and the gauge pressure has increased to 2.72x106 Pa. Compute the final temperature.

51. Problems
7. A welder using a tank of volume m3 fills it with oxygen (molar mass 32.0 g/mol) at a gauge pressure of 3.00x105 Pa and temperature of 37oC. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is 22oC, the gauge pressure of the oxygen in the tank is 1.80x105 Pa. Find (a) the initial mass of oxygen and (b) the mass of oxygen that has leaked out.
8 A large cylindrical tank contains m3 of nitrogen gas at 27oC and 7.50x103 Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to m3 and the temperature is increased to 157°C?

52. Problems
9. You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds L. The pressure of the gas inside the balloon equals air pressure (1.00 atm). (a) If the air inside the balloon is at a constant 22oC and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts? (b) Repeat part (a) if the gas is helium rather than air
10. An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at 22oC to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is 32.0 g/mol. (a) How many moles of oxygen does this canister hold? (b) For someone lifting this canister, by how many kilograms does this gas increase the mass to be lifted?

53. Problems
11. The gas inside a balloon will always have a pressure nearly equal to atmospheric pressure, since that is the pressure applied to the outside of the balloon. You fill a balloon with helium (a nearly ideal gas) to a volume of L at 19oC. What is the volume of the balloon if you cool it to the boiling point of liquid nitrogen (77.3 K)?
12. An ideal gas has a density of 1.33𝑥 10 −6 g/cm3 at 1.00𝑥 10 −3 atm and 20oC. Identify the gas.
13. If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003°C and the pressure is 92 atm?

54. Problems
14. A diver observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is 4oC, and the temperature at the surface is 23oC. (a) What is the ratio of the volume of the bubble as it reaches the surface to its volume at the bottom? (b) Would it be safe for the diver to hold his breath while ascending from the bottom of the lake to the surface? Why or why not?
15. A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at 23oC, to what temperature can the gas be warmed before the tank ruptures? Ignore the thermal expansion of the tank. (b) Based on your answer to part (a), is it reasonable to ignore the thermal expansion of the tank? Explain..
16. Three moles of an ideal gas are in a rigid cubical box with sides of length m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20oC? (b) What is the force when the temperature of the gas is increased to 100oC?

55. Problems
17. With the assumption that the air temperature is a uniform 0.0°C, what is the density of the air at an altitude of 1.00 km as a percentage of the density at the surface?
18. (a) Calculate the mass of nitrogen present in a volume of 3000 cm3 if the gas is at 22.0°C and the absolute pressure of 2.00x10-13 atm is a partial vacuum easily obtained in laboratories. (b) What is the density (in kg/m3) of the N2 ?

56. eNd

57. eNd