# Differences

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 phy131studiof15:lectures:chapter21 [2015/11/16 13:31]mdawber [Path dependence of the work] phy131studiof15:lectures:chapter21 [2015/11/18 09:21] (current)mdawber [Vibrational degrees of freedom] Both sides previous revision Previous revision 2015/11/18 09:21 mdawber [Vibrational degrees of freedom] 2015/11/18 09:21 mdawber [Molar Specific Heat for Gases] 2015/11/18 09:20 mdawber [Molar Specific Heat for Gases] 2015/11/18 09:19 mdawber [Isobaric and Isovolumetric processes] 2015/11/18 09:08 mdawber [Constant volume molar heat capacity for an ideal gas] 2015/11/18 09:07 mdawber [21.P.047] 2015/11/16 13:34 mdawber [Quasistatic adiabatic expansion of a Gas] 2015/11/16 13:33 mdawber [Vibrational degrees of freedom] 2015/11/16 13:31 mdawber [Path dependence of the work] 2015/11/16 13:09 mdawber [Latent Heat] 2015/11/16 13:08 mdawber [Systems] 2015/07/22 12:46 mdawber [Latent Heat] 2015/07/22 12:31 mdawber created Next revision Previous revision 2015/11/18 09:21 mdawber [Vibrational degrees of freedom] 2015/11/18 09:21 mdawber [Molar Specific Heat for Gases] 2015/11/18 09:20 mdawber [Molar Specific Heat for Gases] 2015/11/18 09:19 mdawber [Isobaric and Isovolumetric processes] 2015/11/18 09:08 mdawber [Constant volume molar heat capacity for an ideal gas] 2015/11/18 09:07 mdawber [21.P.047] 2015/11/16 13:34 mdawber [Quasistatic adiabatic expansion of a Gas] 2015/11/16 13:33 mdawber [Vibrational degrees of freedom] 2015/11/16 13:31 mdawber [Path dependence of the work] 2015/11/16 13:09 mdawber [Latent Heat] 2015/11/16 13:08 mdawber [Systems] 2015/07/22 12:46 mdawber [Latent Heat] 2015/07/22 12:31 mdawber created Line 162: Line 162: ===== Isobaric and Isovolumetric processes ===== ===== Isobaric and Isovolumetric processes ===== - We can also consider processes that occur at constant pressure, referred to as isobaric processes, and those which occur at constant volume, referred to as isovolumetric. + We can also consider processes that occur at constant pressure, referred to as isobaric processes, and those which occur at constant volume, referred to as isovolumetric ​or isochoric. ===== Work done in changing the volume of a gas ===== ===== Work done in changing the volume of a gas ===== Line 203: Line 203: {{pathdependenetwork.png}} {{pathdependenetwork.png}} - - ===== 21.P.047 ===== Line 229: Line 227: ===== Molar Specific Heat for Gases ===== ===== Molar Specific Heat for Gases ===== - In our last lecture we introduced the [[phy141:​lectures:​35&#​specific_heat_capacity|specific heat]] which gives the [[wp>​Heat_capacity|heat capacity]] heat capacity of a material per unit mass. Here we will use molar specific heats for gases at constant pressure $c_{P,m}$ and constant volume $c_{V,m}$ and explain the difference between these on the basis of the first law of thermodynamics. + We previously ​introduced the specific heat which gives the [[wp>​Heat_capacity|heat capacity]] heat capacity of a material per unit mass. Here we will use molar specific heats for gases at constant pressure $c_{P,m}$ and constant volume $c_{V,m}$ and explain the difference between these on the basis of the first law of thermodynamics. If we increase the temperature of a gas by $\Delta T$ at constant volume $Q_{V}$ then the first law tells us that If we increase the temperature of a gas by $\Delta T$ at constant volume $Q_{V}$ then the first law tells us that Line 266: Line 264: This prediction is very good for ideal monatomic gases, but gives values too low for more complicated molecules. This prediction is very good for ideal monatomic gases, but gives values too low for more complicated molecules. + + + ===== 21.P.047 ===== + ===== Equipartition of energy ===== ===== Equipartition of energy ===== Line 281: Line 283: ===== Vibrational degrees of freedom ===== ===== Vibrational degrees of freedom ===== - As well as moving and rotating molecules can vibrate. However these modes are typically "​frozen out" in simple molecules at room temperature. As molecules get more complicated the vibrational modes start to contribute to the specific heat. If we cool a gas down we can the rotational degrees of freedom in gas can also become frozen. Quantum theory is required to explain why the number of active modes is dependent on temperature! + As well as moving and rotating molecules can vibrate. However these modes are typically "​frozen out" in simple molecules at room temperature. As molecules get more complicated the vibrational modes start to contribute to the specific heat. If we cool a gas down the rotational degrees of freedom in gas can also become frozen. Quantum theory is required to explain why the number of active modes is dependent on temperature! {{DiatomicSpecHeat1.png?​600}} {{DiatomicSpecHeat1.png?​600}} + + ===== 21.P.050 ===== ===== Quasistatic adiabatic expansion of a Gas ===== ===== Quasistatic adiabatic expansion of a Gas ===== Line 314: Line 318: which gives $PV^{\gamma}=\mathrm{constant}$ which gives $PV^{\gamma}=\mathrm{constant}$ + + ===== 21.P.053 ===== +