Chapter 15 Thermodynamics 15 1 Thermodynamic Systems and Their Surroundings Thermodynamics is the branch of physics that is built upon the fundamental laws that heat and work obey The collection of objects on which attention is being focused is called the system while everything else in the environment is called the surroundings Walls that permit heat flow are called diathermal walls while walls that do not permit heat flow are called adiabatic walls To understand thermodynamics it is necessary to describe the state of a system 15 2 The Zeroth Law of Thermodynamics Two systems are said to be in thermal equilibrium if there is no heat flow between then when they are brought into contact Temperature is the indicator of thermal equilibrium in the sense that there is no net flow of heat between two systems in thermal contact that have the same temperature 15 2 The Zeroth Law of Thermodynamics THE ZEROTH LAW OF THERMODYNAMICS Two systems individually in thermal equilibrium with a third system are in thermal equilibrium with each other 15 3 The First Law of Thermodynamics Suppose that a system gains heat Q and that is the only effect occurring Consistent with the law of conservation of energy the internal energy of the system changes U U f U i Q Heat is positive when the system gains heat and negative when the system loses heat 15 3 The First Law of Thermodynamics If a system does work W on its surroundings and there is no heat flow conservation of energy indicates that the internal energy of the system will decrease U U f U i W Work is positive when it is done by the system and negative when it is done on the system 15 3 The First Law of Thermodynamics THE FIRST LAW OF THERMODYNAMICS The internal energy of a system changes due to heat and work U U f U i Q W Heat is positive when the system gains heat and negative when the system loses heat Work is positive when it is done by the system and negative when it is done on the system 15 3 The First Law of Thermodynamics Example 1 Positive and Negative Work In part a of figure the system gains 1500J of heat and 2200J of work is done by the system on its surroundings In part b the system also gains 1500J of heat but 2200J of work is done on the system In each case determine the change in internal energy of the system 15 3 The First Law of Thermodynamics a U Q W 1500 J 2200 J 700 J b U Q W 1500 J 2200 J 3700 J 15 3 The First Law of Thermodynamics Example 2 An Ideal Gas The temperature of three moles of a monatomic ideal gas is reduced from 540K to 350K as 5500J of heat flows into the gas Find a the change in internal energy and b the work done by the gas U U f U i Q W U 32 nRT 15 3 The First Law of Thermodynamics a U 32 nRT f 32 nRTi 32 3 0 mol 8 31 J mol K 350 K 540 K 7100 J b W Q U 5500 J 7100 J 12600 J 15 4 Thermal Processes A quasi static process is one that occurs slowly enough that a uniform temperature and pressure exist throughout all regions of the system at all times isobaric constant pressure isochoric constant volume isothermal constant temperature adiabatic no transfer of heat 15 4 Thermal Processes An isobaric process is one that occurs at constant pressure W Fs P As P V Isobaric process W P V P V f Vi 15 4 Thermal Processes Example 3 Isobaric Expansion of Water One gram of water is placed in the cylinder and the pressure is maintained at 2 0x105Pa The temperature of the water is raised by 31oC The water is in the liquid phase and expands by the small amount of 1 0x10 8m3 Find the work done and the change in internal energy 15 4 Thermal Processes W P V 2 0 105 Pa 1 0 10 8 m 3 0 0020J U Q W 130 J 0 0020 J 130 J Q mc T 0 0010 kg 4186 J kg C 31 C 130 J 15 4 Thermal Processes W P V P V f Vi 15 4 Thermal Processes isochoric constant volume U Q W Q W 0 15 4 Thermal Processes Example 4 Work and the Area Under a Pressure Volume Graph Determine the work for the process in which the pressure volume and temperature of a gas are changed along the straight line in the figure The area under a pressure volume graph is the work for any kind of process 15 4 Thermal Processes Since the volume increases the work is positive Estimate that there are 8 9 colored squares in the drawing W 8 9 2 0 105 Pa 1 0 10 4 m 3 180 J 15 5 Thermal Processes Using and Ideal Gas ISOTHERMAL EXPANSION OR COMPRESSION Isothermal expansion or compression of an ideal gas Vf W nRT ln Vi 15 5 Thermal Processes Using and Ideal Gas Example 5 Isothermal Expansion of an Ideal Gas Two moles of the monatomic gas argon expand isothermally at 298K from and initial volume of 0 025m3 to a final volume of 0 050m3 Assuming that argon is an ideal gas find a the work done by the gas b the change in internal energy of the gas and c the heat supplied to the gas 15 5 Thermal Processes Using and Ideal Gas a Vf W nRT ln Vi 0 050 m 3 3400 J 2 0 mol 8 31 J mol K 298 K ln 3 0 025 m b c U 32 nRT f 32 nRTi 0 U Q W Q W 3400 J 15 5 Thermal Processes Using and Ideal Gas ADIABATIC EXPANSION OR COMPRESSION Adiabatic expansion or compression of a monatomic ideal gas Adiabatic expansion or compression of a monatomic ideal gas W 32 nR Ti T f PiVi Pf V f cP cV 15 6 Specific Heat Capacities To relate heat and temperature change in solids and liquids we used Q mc T specific heat capacity The amount of a gas is conveniently expressed in moles so we write the following analogous expression Q Cn T molar specific heat capacity 15 6 Specific Heat Capacities For gases it is necessary to distinguish between the molar specific heat capacities which apply to the conditions of constant pressure and constant volume CV C P U 32 nRT Qconstant pressure U W 32 nR T f Ti nR T f Ti 52 nR T first law of thermodynamics constant pressure for a monatomic ideal gas W P V C P 52 R 15 6 Specific Heat Capacities U 32 nRT Qconstant v olume U W 32 nR T f Ti 0 32 nR T first law of thermodynamics constant pressure for a monatomic ideal gas monatomic ideal gas any ideal gas CV 32 R C P 52 R 5 …