Thermodynamics
Thermodynamics SOME DEFINITIONS: • THERMO – related to heat • DYNAMICS – the study of motion • SYSTEM – an object or set of objects • ENVIRONMENT – the rest of the universe • MICROSCOPIC – at an atomic or molecular level • MACROSCOPIC – at a level detectable by our senses THERMODYNAMICS Ø is the study of the relationship between heat and motion. Ø is a macroscopic description of the properties of a system using state variables (e.g. volume, temperature, pressure) Atoms are in constant motion, which increases with temperature.
The Phases of Matter + - + - + - - + - + - + - + - + - - + - + - + + -- + - + - + + -- + - + - + + -- + - + - + + -- + - + + + +- + - + - + + -- + - + -+ -- + - + - + + + - + - + - + -
Solid
Liquid
Gas or Vapor
Plasma
Increasing Temperature Solids and liquids composed of atoms joined together at distances of about 10-10 m by attractive electrical forces. In gases, vapors and plasmas, the atoms, molecules or ions are in random motion.
Temperature Temperature • is a measure of how hot or cold an object is. • is measured by a thermometer. Thermometers are based on physical properties of objects that change with temperature, for example: Ø Ø Ø Ø Ø
volume of a liquid length of a solid pressure of a gas electrical resistance of a solid electrical potential difference between two solids.
Common Temperature Scales Fahrenheit: • Based on the ability of farm animals to survive without attention (0âF is the coldest and 100âF is the hottest). Celsius or Centigrade: • Based on the physical properties of water on the earth’s surface at sea level (0âC is the freezing point and 100âC is the boiling point). T(âC) = (5/9)[T(âF) – 32] T (âF) = (9/5)T(âC) + 32
Zero’th Law of Thermodynamics Our experience tells us that objects placed in contact will eventually reach the same temperature. We say that they are then in thermal equilibrium. This is the basis for The Zero’th Law of Thermodynamics: If two objects A and B are in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other. Objects or systems in thermal equilibrium have the same temperature. This is the physical basis for the definition of temperature.
• Is it possible for two objects to be in thermal equilibrium if they are not touching each other? • Can objects that have different temperatures be in thermal equilibrium with each other?
Most materials expand when heated: Ø The average distance between atoms increases as the temperature is raised. Ø The increase is proportional to the change in temperature (over a small range).
Consider an object of length Li at temperature Ti Ø If the object is heated or cooled to temperature Tf Lf – Li = α Li (Tf – Ti) or ∆L = α Li ∆T α = coefficient of linear expansion [ºC-1] (α is a property of the material)
Thermal Expansion of Solids and Liquids Material
α (ºC -1)
Glass
9 x 10-6
Concrete
12 x 10-6
Copper
17 x 10-6
Lead
29 x 10-6
Mercury
1.8x 10-4
Gasoline
3.2 x 10-4
For the same temperature change, the thermal expansion of liquids is much greater than that of solids (> 10 times). Area Expansion: ∆A = 2α Ai ∆T Volume Expansion ∆V = 3α Vi ∆T
Liquid water has an unusual property. Density of Water 1 g/(cm**3)
0.99 0.98 0.97 0.96 0.95 0
4
12
20
50 100
Temperature in Celsius
• Water contracts when heated from 0ºC to 4ºC, then expands when heated from 4 ºC to 100 ºC. • Just above the freezing point, the coldest (and least dense) water rises to the surface, and lakes freeze from the surface downward. • This unusual property permits aquatic life on earth to survive winter!
• Heat can stress materials if no allowance is made for thermal expansion: 1 F L0 DL = E A DL = a L0 DT 1 F L0 = a L0 DT E A F = a EDT A
E = Young’s Modulus Thermal Expansion
Thermal Stress
The volume occupied by any gas at constant pressure is a linear function of temperature, which always extrapolates to zero at –273.15 ºC. This is called Charles’s Law and is the basis for the absolute or Kelvin temperature scale: T(K) = T(ºC) + 273.15
Absolute or Kelvin Temperature Scale Ø The absolute or Kelvin scale is the true physical temperature scale. Ø T = -273.15 ºC = 0 K is the lowest temperature that can be defined for any physical system. Ø Absolute zero of temperature (0 K) is a theoretical limit that can never be reached in a physical system. Ø Experiments on Bose-Einstein Condensation in gases have reached the nano-Kelvin (10-9 K) range (1998, 2001 Nobel Prizes in physics)!
Ø The degree steps in the Celsius and Kelvin scales are chosen to be the same: ∆T(ºC) = ∆T(K).
Ø The relationship between pressure P, volume V and temperature T of a system is called its equation of state. Ø An ideal gas is one whose equation of state is simple: PV = nRT n = number of moles (6.023 x 1023 molecules) R = universal gas constant = 8.31 J/(mole K)
Ø Most gases near room temperature and atmospheric pressure behave as ideal gases.
• NA = 6.023 x 1023 = Avogadro’s number • 1 mole is the quantity of any gas that contains Avogadro’s number of atoms or molecules. • The gram-molecular-weight M of a substance is the mass of one mole of that substance: Ø Helium (He) M = 4 g/mole Ø Nitrogen (N2) M = 28 g/mole Ø Oxygen (O2) M = 32 g/mole
• For a gas containing N atoms or molecules, the number of moles n = N/NA. • The ideal gas law: PV = nRT = (N/NA)RT = N(R/NA)T = NkBT where kB = R/NA = 1.38 x 10-23 J/K (Boltzmann’s constant) • The ideal gas law may be expressed: PV = NkBT (N = number of atoms or molecules) PV = nRT (n = number of moles)
For a ideal gas: INITIAL STATE (1) P1, V1, T1, n1 P1V1 = n1RT1 R = P1V1/n1T1
FINAL STATE (2) P2, V2, T2, n2 P2V2 = n2RT2 R = P2V2/n2T2
P1V1/n1T1 = P2V2/n2T2
(n variable)
If n1 = n2: P1V1/T1 = P2V2/T2
(n fixed)
Problem 17-34. If 18.75 mol of helium gas is at 10.0ºC and a gauge pressure of 0.350 atm., calculate a) The volume of the helium gas under these conditions. b) The temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.
• An ideal gas in a sealed bottle at temperature T occupies a volume V, and exerts a pressure P on the walls of the bottle. What will happen to the pressure if the temperature is doubled? • Instead of a sealed container, the gas is contained in a test tube with a movable piston on one end. The temperature is then halved. What will happen to a) the pressure? b) the volume?
The Phases of Matter + - + - + - - + - + - + - + - + - - + - + - + + -- + - + - + + -- + - + - + + -- + - + - + + -- + - + + + +- + - + - + + -- + - + -+ -- + - + - + + + - + - + - + -
Solid
Liquid
Gas or Vapor
Plasma
Increasing Temperature Solids and liquids composed of atoms joined together at distances of about 10-10 m by attractive electrical forces. In gases, vapors and plasmas, the atoms, molecules or ions are in random motion.
Temperature Temperature • is a measure of how hot or cold an object is. • is measured by a thermometer. Thermometers are based on physical properties of objects that change with temperature, for example: Ø Ø Ø Ø Ø
volume of a liquid length of a solid pressure of a gas electrical resistance of a solid electrical potential difference between two solids.
Common Temperature Scales Fahrenheit: • Based on the ability of farm animals to survive without attention (0âF is the coldest and 100âF is the hottest). Celsius or Centigrade: • Based on the physical properties of water on the earth’s surface at sea level (0âC is the freezing point and 100âC is the boiling point). T(âC) = (5/9)[T(âF) – 32] T (âF) = (9/5)T(âC) + 32
Zero’th Law of Thermodynamics Our experience tells us that objects placed in contact will eventually reach the same temperature. We say that they are then in thermal equilibrium. This is the basis for The Zero’th Law of Thermodynamics: If two objects A and B are in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other. Objects or systems in thermal equilibrium have the same temperature. This is the physical basis for the definition of temperature.
• Is it possible for two objects to be in thermal equilibrium if they are not touching each other? • Can objects that have different temperatures be in thermal equilibrium with each other?
Most materials expand when heated: Ø The average distance between atoms increases as the temperature is raised. Ø The increase is proportional to the change in temperature (over a small range).
Consider an object of length Li at temperature Ti Ø If the object is heated or cooled to temperature Tf Lf – Li = α Li (Tf – Ti) or ∆L = α Li ∆T α = coefficient of linear expansion [ºC-1] (α is a property of the material)
Thermal Expansion of Solids and Liquids Material
α (ºC -1)
Glass
9 x 10-6
Concrete
12 x 10-6
Copper
17 x 10-6
Lead
29 x 10-6
Mercury
1.8x 10-4
Gasoline
3.2 x 10-4
For the same temperature change, the thermal expansion of liquids is much greater than that of solids (> 10 times). Area Expansion: ∆A = 2α Ai ∆T Volume Expansion ∆V = 3α Vi ∆T
Liquid water has an unusual property. Density of Water 1 g/(cm**3)
0.99 0.98 0.97 0.96 0.95 0
4
12
20
50 100
Temperature in Celsius
• Water contracts when heated from 0ºC to 4ºC, then expands when heated from 4 ºC to 100 ºC. • Just above the freezing point, the coldest (and least dense) water rises to the surface, and lakes freeze from the surface downward. • This unusual property permits aquatic life on earth to survive winter!
• Heat can stress materials if no allowance is made for thermal expansion: 1 F L0 DL = E A DL = a L0 DT 1 F L0 = a L0 DT E A F = a EDT A
E = Young’s Modulus Thermal Expansion
Thermal Stress
The volume occupied by any gas at constant pressure is a linear function of temperature, which always extrapolates to zero at –273.15 ºC. This is called Charles’s Law and is the basis for the absolute or Kelvin temperature scale: T(K) = T(ºC) + 273.15
Absolute or Kelvin Temperature Scale Ø The absolute or Kelvin scale is the true physical temperature scale. Ø T = -273.15 ºC = 0 K is the lowest temperature that can be defined for any physical system. Ø Absolute zero of temperature (0 K) is a theoretical limit that can never be reached in a physical system. Ø Experiments on Bose-Einstein Condensation in gases have reached the nano-Kelvin (10-9 K) range (1998, 2001 Nobel Prizes in physics)!
Ø The degree steps in the Celsius and Kelvin scales are chosen to be the same: ∆T(ºC) = ∆T(K).
Ø The relationship between pressure P, volume V and temperature T of a system is called its equation of state. Ø An ideal gas is one whose equation of state is simple: PV = nRT n = number of moles (6.023 x 1023 molecules) R = universal gas constant = 8.31 J/(mole K)
Ø Most gases near room temperature and atmospheric pressure behave as ideal gases.
• NA = 6.023 x 1023 = Avogadro’s number • 1 mole is the quantity of any gas that contains Avogadro’s number of atoms or molecules. • The gram-molecular-weight M of a substance is the mass of one mole of that substance: Ø Helium (He) M = 4 g/mole Ø Nitrogen (N2) M = 28 g/mole Ø Oxygen (O2) M = 32 g/mole
• For a gas containing N atoms or molecules, the number of moles n = N/NA. • The ideal gas law: PV = nRT = (N/NA)RT = N(R/NA)T = NkBT where kB = R/NA = 1.38 x 10-23 J/K (Boltzmann’s constant) • The ideal gas law may be expressed: PV = NkBT (N = number of atoms or molecules) PV = nRT (n = number of moles)
For a ideal gas: INITIAL STATE (1) P1, V1, T1, n1 P1V1 = n1RT1 R = P1V1/n1T1
FINAL STATE (2) P2, V2, T2, n2 P2V2 = n2RT2 R = P2V2/n2T2
P1V1/n1T1 = P2V2/n2T2
(n variable)
If n1 = n2: P1V1/T1 = P2V2/T2
(n fixed)
Problem 17-34. If 18.75 mol of helium gas is at 10.0ºC and a gauge pressure of 0.350 atm., calculate a) The volume of the helium gas under these conditions. b) The temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.
• An ideal gas in a sealed bottle at temperature T occupies a volume V, and exerts a pressure P on the walls of the bottle. What will happen to the pressure if the temperature is doubled? • Instead of a sealed container, the gas is contained in a test tube with a movable piston on one end. The temperature is then halved. What will happen to a) the pressure? b) the volume?
