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1 Zeroth Law of Thermodynamics If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other B C A C A B

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2 Zeroth Law of Thermodynamics, Example Object C (thermometer) is placed in contact with A until they achieve thermal equilibrium The reading on C is recorded Object C is then placed in contact with object B until they achieve thermal equilibrium The reading on C is recorded again If the two readings are the same, A and B are also in thermal equilibrium

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3 Temperature (Technical) Temperature can be thought of as the property that determines whether an object is in thermal equilibrium with other objects Temperature can be thought of as the property that determines whether an object is in thermal equilibrium with other objects Two objects in thermal equilibrium with each other are at the same temperature Two objects in thermal equilibrium with each other are at the same temperature If two objects have different temperatures, they are not in thermal equilibrium with each other If two objects have different temperatures, they are not in thermal equilibrium with each other

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4 Thermometers A thermometer is a device that is used to measure the temperature of a system A thermometer is a device that is used to measure the temperature of a system Thermometers are based on the principle that some physical property of a system changes as the systems temperature changes Thermometers are based on the principle that some physical property of a system changes as the systems temperature changes

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5 Thermometers, cont These properties include: These properties include: The volume of a liquid The volume of a liquid The dimensions of a solid The dimensions of a solid The pressure of a gas at a constant volume The pressure of a gas at a constant volume The volume of a gas at a constant pressure The volume of a gas at a constant pressure The electric resistance of a conductor The electric resistance of a conductor The color of an object The color of an object A temperature scale can be established on the basis of any of these physical properties A temperature scale can be established on the basis of any of these physical properties

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6 Celsius Scale The ice point of water is defined to be 0 o C The ice point of water is defined to be 0 o C The steam point of water is defined to be 100 o C The steam point of water is defined to be 100 o C The length of the column between these two points is divided into 100 increments, called degrees The length of the column between these two points is divided into 100 increments, called degrees

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7 Constant Volume Gas Thermometer The physical change exploited is the variation of pressure of a fixed volume gas as its temperature changes The physical change exploited is the variation of pressure of a fixed volume gas as its temperature changes The volume of the gas is kept constant by raising or lowering the reservoir B to keep the mercury level at A constant The volume of the gas is kept constant by raising or lowering the reservoir B to keep the mercury level at A constant

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8 Constant Volume Gas Thermometer, cont To find the temperature of a substance, the gas flask is placed in thermal contact with the substance To find the temperature of a substance, the gas flask is placed in thermal contact with the substance The pressure is found on the graph The pressure is found on the graph The temperature is read from the graph The temperature is read from the graph

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9 Absolute Zero The thermometer readings are virtually independent of the gas used The thermometer readings are virtually independent of the gas used If the lines for various gases are extended, the pressure is always zero when the temperature is If the lines for various gases are extended, the pressure is always zero when the temperature is – o C This temperature is called absolute zero This temperature is called absolute zero

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

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11 An Ideal Gas For gases, the interatomic forces within the gas are very weak For gases, the interatomic forces within the gas are very weak We can imagine these forces to be nonexistent We can imagine these forces to be nonexistent Note that there is no equilibrium separation for the atoms Note that there is no equilibrium separation for the atoms Thus, no standard volume at a given temperature Thus, no standard volume at a given temperature

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12 Ideal Gas, cont For a gas, the volume is entirely determined by the container holding the gas For a gas, the volume is entirely determined by the container holding the gas Equations involving gases will contain the volume, V, as a variable Equations involving gases will contain the volume, V, as a variable This is instead of focusing on V This is instead of focusing on V

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13 Gas: Equation of State It is useful to know how the volume, pressure and temperature of the gas of mass m are related It is useful to know how the volume, pressure and temperature of the gas of mass m are related The equation that interrelates these quantities is called the equation of state The equation that interrelates these quantities is called the equation of state These are generally quite complicated These are generally quite complicated If the gas is maintained at a low pressure, the equation of state becomes much easier If the gas is maintained at a low pressure, the equation of state becomes much easier This type of a low density gas is commonly referred to as an ideal gas This type of a low density gas is commonly referred to as an ideal gas

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14 The Mole The amount of gas in a given volume is conveniently expressed in terms of the number of moles The amount of gas in a given volume is conveniently expressed in terms of the number of moles One mole of any substance is that amount of the substance that contains Avogadros number of constituent particles One mole of any substance is that amount of the substance that contains Avogadros number of constituent particles Avogadros number N A = x Avogadros number N A = x The constituent particles can be atoms or molecules The constituent particles can be atoms or molecules

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15 Moles, cont The number of moles can be determined from the mass of the substance: n = m /M The number of moles can be determined from the mass of the substance: n = m /M M is the molar mass of the substance M is the molar mass of the substance m is the mass of the sample m is the mass of the sample n is the number of moles n is the number of moles Example: H 2 : 2g/mol, O 2 : 32g/mol, H 2 O: 18g/mol

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16 Gas Laws When a gas is kept at a constant temperature, its pressure is inversely proportional to its volume (Boyles law) When a gas is kept at a constant temperature, its pressure is inversely proportional to its volume (Boyles law) P 1 V 1 = P 2 V T = const. When a gas is kept at a constant pressure, its volume is directly proportional to its temperature (Charles and Gay-Lussacs law) When a gas is kept at a constant pressure, its volume is directly proportional to its temperature (Charles and Gay-Lussacs law) V 1 /V 2 = T 1 /T P = const.

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17 Ideal Gas Law The equation of state for an ideal gas combines and summarizes the other gas laws The equation of state for an ideal gas combines and summarizes the other gas laws PV = nRT This is known as the ideal gas law This is known as the ideal gas law R is a constant, called the Universal Gas Constant R is a constant, called the Universal Gas Constant R = J/mol K R = J/mol K From this, you can determine that 1 mole of any gas at atmospheric pressure and at 0 o C is 22.4 L From this, you can determine that 1 mole of any gas at atmospheric pressure and at 0 o C is 22.4 L

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18 Ideal Gas Law, cont The ideal gas law is often expressed in terms of the total number of molecules, N, present in the sample The ideal gas law is often expressed in terms of the total number of molecules, N, present in the sample PV = nRT = (N/N A ) RT = Nk B T PV = nRT = (N/N A ) RT = Nk B T k B is Boltzmanns constant k B is Boltzmanns constant k B = 1.38 x J/K k B = 1.38 x J/K It is common to call P, V, and T the thermodynamic variables of an ideal gas It is common to call P, V, and T the thermodynamic variables of an ideal gas

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19 Example A spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and having a volume of cm 3 is at 22 o C. It is then tossed into an open fire. When the temperature of the gas in the can reaches 195 o C, what is the pressure inside the can? Assume any change in the volume of the can is negligible. A spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and having a volume of cm 3 is at 22 o C. It is then tossed into an open fire. When the temperature of the gas in the can reaches 195 o C, what is the pressure inside the can? Assume any change in the volume of the can is negligible.

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