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Zeroth Law of Zeroth Law of ThermodynamicsThermodynamics

► If objects A and B are separately in If objects A and B are separately in thermal equilibrium with a third object thermal equilibrium with a third object C, then A and B are in thermal C, then A and B are in thermal equilibrium with each otherequilibrium with each other

BC

A

CA

B

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Zeroth Law of Zeroth Law of Thermodynamics, Thermodynamics,

ExampleExample

► Object C (thermometer) is placed in contact with A Object C (thermometer) is placed in contact with A until they achieve thermal equilibriumuntil they achieve thermal equilibrium The reading on C is recordedThe reading on C is recorded

► Object C is then placed in contact with object B until Object C is then placed in contact with object B until they achieve thermal equilibriumthey achieve thermal equilibrium The reading on C is recorded againThe reading on C is recorded again

► If the two readings are the same, A and B are also in If the two readings are the same, A and B are also in thermal equilibriumthermal equilibrium

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Temperature (Technical)Temperature (Technical)

►Temperature Temperature can be thought of as can be thought of as the property that determines whether the property that determines whether an object is in thermal equilibrium with an object is in thermal equilibrium with other objects other objects

►Two objects in thermal equilibrium Two objects in thermal equilibrium with each other are at the same with each other are at the same temperaturetemperature If two objects have different If two objects have different

temperatures, they are not in thermal temperatures, they are not in thermal equilibrium with each otherequilibrium with each other

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ThermometersThermometers

►A A thermometerthermometer is a device that is is a device that is used to measure the temperature of a used to measure the temperature of a systemsystem

►Thermometers are based on the Thermometers are based on the principle that some physical property principle that some physical property of a system changes as the system’s of a system changes as the system’s temperature changestemperature changes

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Thermometers, contThermometers, cont

►These properties include:These properties include: The volume of a liquidThe volume of a liquid The dimensions of a solidThe dimensions of a solid The pressure of a gas at a constant volumeThe pressure of a gas at a constant volume The volume of a gas at a constant pressureThe volume of a gas at a constant pressure The electric resistance of a conductorThe electric resistance of a conductor The color of an objectThe color of an object

► A temperature scale can be established on the A temperature scale can be established on the basis of any of these physical propertiesbasis of any of these physical properties

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Celsius ScaleCelsius Scale

► The ice point of water is defined to be 0The ice point of water is defined to be 0oo C C► The steam point of water is defined to be 100The steam point of water is defined to be 100o o CC

► The length of the column between these two The length of the column between these two points is divided into 100 increments, called points is divided into 100 increments, called degreesdegrees

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Constant Volume Gas Constant Volume Gas ThermometerThermometer

► The physical change The physical change exploited is the variation exploited is the variation of pressure of a fixed of pressure of a fixed volume gas as its volume gas as its temperature changestemperature changes

► The volume of the gas is The volume of the gas is kept constant by raising kept constant by raising or lowering the reservoir B or lowering the reservoir B to keep the mercury level to keep the mercury level at A constantat A constant

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Constant Volume Gas Constant Volume Gas Thermometer, contThermometer, cont

► To find the To find the temperature of a temperature of a substance, the gas substance, the gas flask is placed in flask is placed in thermal contact thermal contact with the substancewith the substance

► The pressure is The pressure is found on the graphfound on the graph

► The temperature is The temperature is read from the graphread from the graph

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Absolute ZeroAbsolute Zero

► The thermometer The thermometer readings are virtually readings are virtually independent of the independent of the gas usedgas used

► If the lines for various If the lines for various gases are extended, gases are extended, the pressure is always the pressure is always zero when the zero when the temperature is temperature is ––273.15273.15oo C C

► This temperature is This temperature is called called absolute zeroabsolute zero

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Phase Diagram of triple point Phase Diagram of triple point of waterof water

The triple point of water occurs at 0.01o C and 4.58 mm (0.06 atm)of mercury

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An Ideal GasAn Ideal Gas

►For gases, the interatomic forces For gases, the interatomic forces within the gas are very weakwithin the gas are very weak We can imagine these forces to be We can imagine these forces to be

nonexistentnonexistent

►Note that there is no equilibrium Note that there is no equilibrium separation for the atomsseparation for the atoms Thus, no “standard” volume at a given Thus, no “standard” volume at a given

temperaturetemperature

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Ideal Gas, contIdeal Gas, cont

►For a gas, the volume is entirely For a gas, the volume is entirely determined by the container holding determined by the container holding the gasthe gas

►Equations involving gases will contain Equations involving gases will contain the volume, the volume, VV, as a variable, as a variable This is instead of focusing on This is instead of focusing on VV

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Gas: Equation of StateGas: Equation of State► It is useful to know how the volume, It is useful to know how the volume,

pressure and temperature of the gas of pressure and temperature of the gas of mass mass mm are related are related

►The equation that interrelates these The equation that interrelates these quantities is called the quantities is called the equation of equation of statestate These are generally quite complicatedThese are generally quite complicated If the gas is maintained at a low pressure, If the gas is maintained at a low pressure,

the equation of state becomes much easierthe equation of state becomes much easier This type of a low density gas is commonly This type of a low density gas is commonly

referred to as an referred to as an ideal gasideal gas

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The MoleThe Mole

►The amount of gas in a given volume The amount of gas in a given volume is conveniently expressed in terms of is conveniently expressed in terms of the number of molesthe number of moles

►One One molemole of any substance is that of any substance is that amount of the substance that contains amount of the substance that contains Avogadro’s numberAvogadro’s number of constituent of constituent particlesparticles Avogadro’s number Avogadro’s number NNAA = 6.022 x 10 = 6.022 x 102323

The constituent particles can be atoms or The constituent particles can be atoms or moleculesmolecules

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Moles, contMoles, cont

►The number of moles can be The number of moles can be determined from the mass of the determined from the mass of the substance: substance: nn = = mm / /MM MM is the molar mass of the substance is the molar mass of the substance mm is the mass of the sample is the mass of the sample nn is the number of moles is the number of moles

Example: Example: HH22: 2g/mol, O: 2g/mol, O22: 32g/mol, H: 32g/mol, H22O: O: 18g/mol18g/mol

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Gas LawsGas Laws

► When a gas is kept at a constant When a gas is kept at a constant temperature, its pressure is inversely temperature, its pressure is inversely proportional to its volume (proportional to its volume (Boyle’s lawBoyle’s law))

PP11VV11 = P = P22VV2 2 @ T = const.@ T = const.

► When a gas is kept at a constant pressure, When a gas is kept at a constant pressure, its volume is directly proportional to its its volume is directly proportional to its temperature (temperature (Charles and Gay-Lussac’s lawCharles and Gay-Lussac’s law))

VV11/V/V22 = T = T11/T/T2 2 @ P = const.@ P = const.

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Ideal Gas LawIdeal Gas Law

► The equation of state for an ideal gas The equation of state for an ideal gas combines and summarizes the other gas lawscombines and summarizes the other gas laws

PVPV = = nRTnRT► This is known as the This is known as the ideal gas lawideal gas law► RR is a constant, called the Universal Gas is a constant, called the Universal Gas

ConstantConstant RR = 8.314 J/mol ∙ K = 8.314 J/mol ∙ K

► From this, you can determine that 1 mole of From this, you can determine that 1 mole of any gas at atmospheric pressure and at 0any gas at atmospheric pressure and at 0oo C C is 22.4 Lis 22.4 L

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Ideal Gas Law, contIdeal Gas Law, cont

► The ideal gas law is often expressed in The ideal gas law is often expressed in terms of the total number of molecules, terms of the total number of molecules, NN, , present in the samplepresent in the sample

► PVPV = = nRTnRT = ( = (NN//NNAA) ) RTRT = = NkNkBBTT kkBB is Boltzmann’s constant is Boltzmann’s constant

kkB B = 1.38 x 10= 1.38 x 10-23-23 J/K J/K

► It is common to call It is common to call PP, , VV, and , and TT the the thermodynamic variablesthermodynamic variables of an ideal gas of an ideal gas

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Example Example

► A spray can containing a propellant gas at A spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and twice atmospheric pressure (202 kPa) and having a volume of 125.00 cmhaving a volume of 125.00 cm33 is at 22 is at 22ooC. C. It is then tossed into an open fire. When It is then tossed into an open fire. When the temperature of the gas in the can the temperature of the gas in the can reaches 195reaches 195ooC, what is the pressure inside C, what is the pressure inside the can? Assume any change in the the can? Assume any change in the volume of the can is negligible.volume of the can is negligible.