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phy141kk:lectures:33-18 [2018/11/25 10:49] (current)
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 +~~SLIDESHOW~~
  
 +====== Fall 2018: Lecture 33 - Heat ======
 +/*
 +
 +----
 +If you need a pdf version of these notes you can get it [[http://​www.ic.sunysb.edu/​class/​phy141md/​lecturepdfs/​141lecture35F11.pdf|here]]
 +
 +===== Video of lecture ====
 +
 +
 +<​html>​
 +<video id="​video"​ width="​640"​ height="​360"​ controls="​true"/>​
 +<source src="​lecturevids/​phy141f13lecture35.mp4"​ type="​video/​mp4"></​source>​
 +<source src="​lecturevids/​phy141f13lecture35.webm"​ type="​video/​webm"></​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/​phy141f13lecture35.mp4"​ />
 +
 + </​object>​
 + 
 +
 +    </​video>​
 +</​html>​
 +
 +*/
 +
 +===== What is heat? =====
 +
 +[[wp>​Heat|Heat]] should not be confused with temperature.
 +
 +Heat is the energy transferred from one body to another due to thermal contact when the bodies are at different temperatures.
 +
 +An early theory of heat was the [[wp>​Caloric_theory|caloric theory]], which suggested that there was a fluid called caloric that was transferred from a hot to a cold body. The idea that there was a particular substance associated with heat would imply conservation of heat.
 +
 +A key player in overturning the caloric theory was [[wp>​James_Prescott_Joule|James Prescott Joule]]. Through number of experiments,​ initially motivated by his interest in using electric motors to power his brewery he was able to the equivalence of energy and heat.
 +
 +===== Units of heat =====
 +
 +As heat is a form of energy it can be measured in Joules (which is the SI unit for heat). ​
 +
 +However its is very common to measure it in calories
 +
 +$1 \mathrm{cal}=4.186 \mathrm{J}$
 +
 +A  calorie $(\mathrm{cal})$ is the amount of heat necessary to raise the temperature of 1 gram of water by 1 $\mathrm{^{o}C}$.
 +
 +Energy in food is often measured in kilocalories $(\mathrm{kcal})$,​ which, somewhat confusingly,​ are refereed to as Calories.
 +
 +Another unit of heat, ironically most commonly used in the United States, is the [[wp>​British_thermal_unit|British thermal units]] or BTU. The exact value of a BTU depends on where you are and how warm it is...but we can take it to be 1054.8 J.
 +
 +===== Heat transfer =====
 +
 +[[wp>​Heat_transfer|Heat transfer]] occurs by several different mechanisms.
 +
 +  * Conduction-Primary mechanism for solids in thermal contact with each other.
 +  * Convection-Movements of molecules in a gas or liquid.
 +  * Radiation-Electromagnetic transmission of heat, does not require a medium. ​
 +
 +===== Conduction =====
 +
 +
 +Conduction occurs by neighboring particles transferring energy from one to another. The ability of a material to conduct heat is measured by a parameter called the [[wp>​Thermal_conductivity|thermal conductivity]],​ $k$. In the case of metal much of the conduction occurs through the free electrons which are also responsible for the electronic conduction. Non-metallic solids can also be good conductors of heat, lattice vibrations can also be an extremely effective way of transferring energy from one part of a material to another. ​
 +
 +  ​
 +The heat flow $\Delta Q$ during a time interval $\Delta t$ in a conductor of length $l$ and area $A$ which connects two object'​s which have temperature $T_{1}$ and $T_{2}$ is
 +
 +$\frac{\Delta Q}{\Delta t}=kA\frac{T_{1}-T_{2}}{l}$
 +
 +which in differential form is
 +
 +$\frac{dQ}{dt}=-kA\frac{dT}{dx}$
 +
 +When dealing with practical situations the thermal conduction properties of a specific piece of building material will often be given as a thermal resistance $R$ where 
 +
 +$R=\frac{l}{k}$
 +
 +and $l$ is the thickness of the piece of the material.
 +
 +
 +===== Convection =====
 +
 +[[wp>​Convective_heat_transfer|Convective heat transfer]] is heat transfer by the bulk motion of fluid.
 +
 +Natural convection currents can occur due to changes in density as the temperature of a fluid changes. ​
 +
 +{{convection.png}}
 +
 +Convection can also be forced, by the use of fans, stirrers or pumps.
 +
 +===== Radiation =====
 +
 +Thermal energy within a material is converted in to electromagnetic radiation.
 +
 +The rate of radiation leaving the surface of a material with area A is given by the [[wp>​Stefan%E2%80%93Boltzmann_law|Stefan-Boltzmann equation]].
 +
 +$\frac{\Delta W}{\Delta t}=\epsilon\sigma A T^{4}$
 +
 +A body also absorbs radiation from it's surroundings with temperature $T_{s}$ according to
 +
 +$\frac{\Delta W}{\Delta t}=\epsilon\sigma A T_{s}^{4}$
 +
 +$\sigma$ is the Stefan-Boltzmann constant
 +
 +$\sigma=5.67\times10^{-8}W/​m^{2}K^4$ and $\epsilon$ is the emissivity of the surface, a perfect surface for emission or asborption (a black surface) has an emissivity of 1, whereas a shiny surface that neither absorbs or transmits would have an emissivity of zero. Most materials are somewhere in between these two limits.
 +
 +If the body is in thermal equilibrium with it's surroundings,​ then $T=T_{s}$, the rate of emission equals the rate of absorption and the rate of heat flow is zero.
 +
 +===== Specific Heat Capacity=====
 +
 +A quantity of heat, $Q$, flowing into an object leads to a change in the temperature of the object, $\Delta T$, which is proportional to it's mass $m$ and a characteristic quantity of the material, it's specific heat, $c$
 +
 +$Q=mc\Delta T$
 +
 +We can see that heat flowing in to an object is positive $\Delta T>0$ and heat flowing out is negative $\Delta T < 0$
 +
 +The specific heat is the [[wp>​Heat_capacity|heat capacity]] per a unit of mass, in SI the units of specific heat are $\mathrm{\frac{J}{kg.K}}$.
 +
 +The specific heat of a material can depend on the conditions, for example the table in your textbook gives specific heats for materials at a fixed pressure per unit mass, the [[wp>​Heat_capacity|table in wikipedia]] gives these and also molar specific heats at constant pressure/​constant volume. We will look at the effect of changes in volume on heat capacity by using the first law of thermodynamics in our next lecture. ​
 +
 +===== Systems =====
 +
 +When considering a set objects in a calorimetry problem we need to consider the boundary conditions on the system.
 +
 +If a system has constant mass, with none either being lost or added, then we can say it is a closed system. This does not necessarily mean that energy cannot enter of leave. A system in which the total amount of energy is conserved is called an isolated system. A system in which both mass and energy can enter or leave is called an open system.
 +
 +The assumption of an isolated system is very useful in problem solving as it says that the sum of the heat transfers in the system must be zero.
 +
 +$\Sigma Q = 0$
 +
 +In a system where the different objects start at different temperatures,​ but eventually come to an equilibrium temperature $T$
 +
 +$\Sigma Q = m_{1}c_{1}(T-T_{i1})+m_{2}c_{2}(T-T_{i2})+..$
 +
 +===== Latent Heat =====
 +
 +To this point we have considered systems where the constituents all stay in the same phase. Phase changes from a low temperature phases to a high temperature phase require a certain amount of heat, called the [[wp>​Latent_heat|latent heat]].
 +
 +The latent heat of of fusion, $L_{f}$, refers to a change from solid to liquid and the latent heat of vaporization,​ $L_{v}$, refers to a change from liquid to gas. The heat required to change a mass $m$ of a substance from one phase to another is 
 +
 +$Q=mL$
 +
 +During a change from one phase to another the temperature of the system remains constant. A good example we know from our everyday experience involves [[http://​hyperphysics.phy-astr.gsu.edu/​hbase/​thermo/​phase.html|heating water from ice]]. By adding ice to water we quickly have the temperature of the solution equilibrate to $0\mathrm{^{o}C}$ and stay there as long as some ice remains.
 +
 +/*
 +===== An experiment to demonstrate the mechanical equivalence of heat  =====
 +
 +If I drop 1 kg of small lead balls through a height of 1m, they should gain kinetic energy equal to $mgh=9.8\mathrm{J}$. When they hit the ground the energy goes into heat, which will mainly go to raise the temperature of the lead balls.
 +
 +The heat capacity of lead is $129 \mathrm{J\,​kg^{-1}K^{-1}}$
 +
 +Therefore if I drop the lead balls 13 times and all the energy goes to heat which is transferred to the balls I should get a $1\mathrm{K}$ temperature rise. Let's see how well this works...
 +*/
 +
 +
 +
 +===== First Law of Thermodynamics =====
 +
 +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 $W$.
 +
 +$\Delta E_{int}=Q-W$
 +
 +The first law is a powerful statement of the conservation of energy, indeed conservation of energy can only be understood once we understand that heat is a transfer of energy.
 +
 +In our next lecture we will apply the first law to several cases and take a more careful look at the specific heat of gases.
phy141kk/lectures/33-18.txt ยท Last modified: 2018/11/25 10:49 by kkumar
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