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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 ==== | ||

+ | |||

+ | |||

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+ | <source src="lecturevids/phy141f13lecture35.mp4" type="video/mp4"></source> | ||

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+ | */ | ||

+ | |||

+ | ===== 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. |