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phy141:lectures:36 [2010/12/02 12:58]
mdawber created
phy141:lectures:36 [2013/11/20 10:07] (current)
mdawber [Next week]
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 ====== Lecture 36 - First Law of Thermodynamics ====== ====== Lecture 36 - First Law of Thermodynamics ======
 +
 +----
 +If you need a pdf version of these notes you can get it [[http://​www.ic.sunysb.edu/​class/​phy141md/​lecturepdfs/​141lecture36F11.pdf|here]]
 +
 +===== Video of lecture ====
 +
 +Unfortunately the 2013 lecture recording did not work, so here is the 2012 version.
 +
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 +<source src="​lecturevids/​phy141f12lecture36.mp4"​ type="​video/​mp4"></​source>​
 +<source src="​lecturevids/​phy141f12lecture36.ogv"​ type="​video/​ogg"></​source>​
 +
 +
 +<object width="​640"​ height="​384"​ type="​application/​x-shockwave-flash"​ data="​player.swf">​
 + <param name="​movie"​ value="​player.swf"​ />
 + <param name="​flashvars"​ value="​file=lecturevids/​phy141f12lecture36.mp4"​ />
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 +
 +    </​video>​
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 +
  
 ===== First Law of Thermodynamics ===== ===== First Law of Thermodynamics =====
  
-The [[http://​en.wikipedia.org/​wiki/​First_law_of_thermodynamics|first law of thermodynamics]],​ dictates how internal energy, heat and work are related to each other. For a closed system the first law states that the change in the internal energy of a system, $\Delta E_{int}$, is the sum of the heat added **to** the system $Q$ and the net work done **by** the system $W$.+The [[wp>First_law_of_thermodynamics|first law of thermodynamics]],​ dictates how internal energy, heat and work are related to each other. For a closed system the first law states that the change in the internal energy of a system, $\Delta E_{int}$, is the sum of the heat added **to** the system $Q$ and the net work done **by** the system $W$.
  
 $\Delta E_{int}=Q-W$ $\Delta E_{int}=Q-W$
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 ===== Isothermal Processes ===== ===== Isothermal Processes =====
  
-An [[http://​en.wikipedia.org/​wiki/​Isothermal_process|isothermal process]] is one which occurs at a constant temperature. In order for such a process ​too occur there should be a [[http://​en.wikipedia.org/​wiki/​Heat_reservoir|heat reservoir]],​ a large body in thermal contact with they system ​that'​s ​temperature will not significantly change as heat is exchanged with it. We will consider a [[http://​en.wikipedia.org/​wiki/​Quasistatic_process|quasistatic process]], which means it occurs slowly enough that the system can be considered to be in equilibrium at any given time. +An [[wp>Isothermal_process|isothermal process]] is one which occurs at a constant temperature. In order for such a process ​to occur there should be a [[wp>Heat_reservoir|heat reservoir]],​ a large body in thermal contact with the system ​which has a temperature ​that will not significantly change as heat is exchanged with it. We will consider a [[wp>Quasistatic_process|quasistatic process]], which means it occurs slowly enough that the system can be considered to be in equilibrium at any given time. 
  
 From the viewpoint of the first law From the viewpoint of the first law
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 $\Delta E_{int}=-W$ $\Delta E_{int}=-W$
  
-Remember that $W$ is the work done by the system, so when a gas expands it does work and theinternal energy, and hence the temperature of the gas decreases. When a gas is compressed, work is done on it so it's temperature increases.+Remember that $W$ is the work done by the system, so when a gas expands it does work and the internal energy, and hence the temperature of the gas decreases. When a gas is compressed, work is done on it so it's temperature increases.
  
 ===== Isobaric and Isovolumetric processes ===== ===== Isobaric and Isovolumetric processes =====
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 If nothing opposes the expansion of the gas then no work is done by the gas when it expands. If the system is also insulated from heat then $Q=W=0$ and the internal energy $E_{int}$ does not change, meaning the temperature does not change, if the gas is ideal. Real gases do show a small decrease in temperature under free expansion, in real gases the internal energy depends a little on pressure and volume as well as temperature. If nothing opposes the expansion of the gas then no work is done by the gas when it expands. If the system is also insulated from heat then $Q=W=0$ and the internal energy $E_{int}$ does not change, meaning the temperature does not change, if the gas is ideal. Real gases do show a small decrease in temperature under free expansion, in real gases the internal energy depends a little on pressure and volume as well as temperature.
  
-This situation is called [[http://​en.wikipedia.org/​wiki/​Free_expansion|free expansion]].+This situation is called [[wp>Free_expansion|free expansion]].
  
 ===== Molar Specific Heat for Gases ===== ===== Molar Specific Heat for Gases =====
  
-In our last lecture we introduced the specific heat which gives the 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.+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.
  
 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 
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 $nc_{P,​m}\Delta T-nc_{V,​m}\Delta T=P(\frac{nR\Delta T}{P})$ → $c_{P,​m}-c_{V,​m}=R$ $nc_{P,​m}\Delta T-nc_{V,​m}\Delta T=P(\frac{nR\Delta T}{P})$ → $c_{P,​m}-c_{V,​m}=R$
  
-Let's recall that $R=8.314\,​\mathrm{J/​mol.K}$ and compare this to the [[http://​en.wikipedia.org/​wiki/​Heat_capacity|table of specific heats]] on Wikipedia.+Let's recall that $R=8.314\,​\mathrm{J/​mol.K}$ and compare this to the [[wp>Heat_capacity|table of specific heats]] on Wikipedia.
  
 ===== Constant volume molar heat capacity for an ideal gas ===== ===== Constant volume molar heat capacity for an ideal gas =====
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 $\Delta E_{int}=\frac{3}{2}nR\Delta T=nc_{V,​m}\Delta T$ → $c_{V,​m}=\frac{3}{2}R=12.471\,​\mathrm{J/​mol.K}$ $\Delta E_{int}=\frac{3}{2}nR\Delta T=nc_{V,​m}\Delta T$ → $c_{V,​m}=\frac{3}{2}R=12.471\,​\mathrm{J/​mol.K}$
  
-We can also compare this to the [[http://​en.wikipedia.org/​wiki/​Heat_capacity|table of specific heats]] on Wikipedia.+We can also compare this to the [[wp>Heat_capacity|table of specific heats]] on Wikipedia.
  
 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.
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 ===== Equipartition of energy ===== ===== Equipartition of energy =====
  
-The [[http://​en.wikipedia.org/​wiki/​Equipartition_theorem|equipartition theorem]] can be used to explain the higher heat capacity of more complicated gases. The equipartition theorem states that energy is equally shared between the different degrees of freedom the molecules in the gas have.+The [[wp>Equipartition_theorem|equipartition theorem]] can be used to explain the higher heat capacity of more complicated gases. The equipartition theorem states that energy is equally shared between the different degrees of freedom the molecules in the gas have.
  
 {{degreesoffreedom.png}} {{degreesoffreedom.png}}
  
-Each degree of translational or rotational freedom contributes $\frac{1}{2}R$ to the molar specific heat.+Each degree of translational or rotational freedom contributes $\frac{1}{2}R$ to the molar specific heat at constant volume.
  
 We can see that diatomic molecules should thus have $c_{V,​m}=\frac{5}{2}R=20.785\mathrm{J/​mol.K}$ We can see that diatomic molecules should thus have $c_{V,​m}=\frac{5}{2}R=20.785\mathrm{J/​mol.K}$
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 which gives $PV^{\gamma}=\mathrm{constant}$ which gives $PV^{\gamma}=\mathrm{constant}$
  
-===== Next week ===== 
- 
-Second law of thermodynamics and entropy...and then prepare for the final exam! 
  
phy141/lectures/36.1291312727.txt · Last modified: 2010/12/02 12:58 by mdawber
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