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Observed that a cannon got really hot when it was being bored. Where did the heat come?

Benjamin Thompson 1798. Observed that a cannon got really hot when it was being bored. Where did the heat come? Lovoisier said that the heat had to flow from someplace.

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Observed that a cannon got really hot when it was being bored. Where did the heat come?

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  1. Benjamin Thompson 1798 • Observed that a cannon got really hot when it was being bored. • Where did the heat come? • Lovoisier said that the heat had to flow from someplace. • But the surroundings were also getting hotter (Heat was actually flowing from the cannon to the air around it). The surroundings should have been getting colder. • But cannon kept on getting hotter the more that it was bored. • Seemingly infinite supply of heat • Postulated that the work done on the cannon by the boring machine was being converted to heat. • Nobody believed him even though it was well known from steam engines that heat could create work. • Regardless he sunk Lavoisiers Caloric Theory

  2. Caloric Theory 1849 when Joule demonstrated that water can be heated by doing (mechanical) work and showed that for every 4186 J of work done, the temperature of water rose by 1C0 per kg.

  3. Scientific Method • Observations - Heat transfers from hot to cold • Hypothesis - A testable explanation that makes a prediction • Experiment - Tests a prediction • Fails then hypothesis/theory needs to be revised or restated • Passes When a preponderance of the evidence supports the hypothesis it can become a theory.

  4. Rudolf Clausius 1850 • Caloric theory (conservation of heat) was shown to be untrue by Thompson. • Joule showed equivalence of Work and Heat. • Clausius reforms Lavoisier’s Caloric theory and comes up with the first law of Thermodynamics (which we’ll go over in great detail in a couple of lectures) The first law of thermodynamics: the internal energy of a system can be changed by doing work on it or by heating/cooling it. U = q + w The conserved quantity is not Heat: The conserved quantity is Energy which can be changed by having heat flow into/out of the system or by work being done on/by the system.

  5. Piston in a cylinder moves by dl due to expansion of gas at pressure p Force on piston: F = p·A Incremental work done: dW = F·dl = p·A dl = p·dV p What is Work?

  6. W = - F Dx Kg m2/s2 = Joule Kg m/s2 m L-atm W = - P DV atm Liters L-atm mol K (0.0825 L-atm/mol K) PV = n R T J/m3 m3 mol (8.31451 J/mol K) Physical Units of Work 1 L-atm = 101.325 J

  7. As piston is displaced by h2 - h1=Dh, volume increases by ADh=DV

  8. What is Heat? • Up to mid-1800’s heat was considered a fluid that flowed from hot objects to cold objects. • A better definition is that it is the energy that flows from hot bodies to cold bodies in order to establish thermal equilibrium. This is called thermal energy. • The term Heat (Q) is properly used to describe energy in transit, that is thermal energy transferred into or out of a system. Heat only makes sense in the context of the process of the transformation from one state to another. It is not a state or equilibrium property of the system.

  9. T(system) goes down T(surr) goes up Directionality of Heat Transfer • Heat always transfer from hotter object to cooler one. • EXOthermic: heat transfers from SYSTEM to SURROUNDINGS.

  10. T(system) goes up T (surr) goes down Directionality of Heat Transfer • Heat always transfer from hotter object to cooler one. • ENDOthermic: heat transfers from SURROUNDINGS to the SYSTEM.

  11. State of the System • The Physical State of a system is completely described by a small number of Macroscopic Variables (m,n,P,V,T,½…). • These variables are called state variables and include pressure, volume, temperature, amount of substance, Internal Energy • In a chemical reaction it is the amounts (concentrations) of the products and reactants, their phases (gas, liquid, solid), Temperature and Pressure.

  12. Equilibrium States State space f i • Thermodynamics is concerned with equilbrium states. • An equilibrium state is one in which macroscopic properties • (E,V,P,T,n1,n2 ,...) do not change with time. Properties are • Either extensive (E,V,n) or intensive (T,P)

  13. c b f a i State Functions for a Mountain Trekker

  14. Rudolf Clausius 1850 • Caloric theory (conservation of heat) was shown to be untrue by Thompson. • Joule showed equivalence of Work and Heat. • Clausius reforms Lavoisier’s Caloric theory and comes up with the first law of Thermodynamics (which we’ll go over in great detail in a couple of lectures) The first law of thermodynamics: the internal energy of a system can be changed by doing work on it or by heating/cooling it. U = q + w The conserved quantity is not Heat: The conserved quantity is Energy which can be changed by having heat flow into/out of the system or by work being done on/by the system.

  15. Melting ice in a glass adiabatically and through stirring.

  16. The Ideal Gas Law In terms of the total number of molecules, N = nNA Avogadro’s number the Boltzmann constant kB= R/NA  1.3810-23 J/K (introduced by Planck in 1899) NA 6.0220451023 The equations of state cannot be derived within the frame of thermodynamics: they can be either considered as experimental observations, or “borrowed” from statistical mechanics. isotherms The P-V diagram – the projection of the surface of the equation of state onto the P-V plane. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

  17. Two asides about the Ideal Gas Law • We mentioned that the ideal gas law could come from observations or from theory. • At the time of the early development of thermodynamics, it had been deduced from observation and in particular 3 laws: Boyle’s Law, Charles Law and Avogadro’s Law • When statistical Mechanics came around in the late 19th century, one of its early successes was reproducing the ideal gas law with the kinetic theory of gases. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAA

  18. Charles’s Law Temperature-Volume Relationship: The volume of a fixed amount of a gas at constant pressure is directly proportional to its Kelvin temperature i.e., if V, then T or V/T =C EOS

  19. Boyle’s Law Pressure-Volume Relationship: For a given amount of a gas at constant temperature, the product of the pressure and the volume is a constant PV = C This gives ideal gas isotherms EOS

  20. … that is, V/n = C EOS Avogadro’s Principle:Mole-Volume Relationship At a fixed temperature and pressure, the volume of a gas is directly proportional to the number of molecules of gas. Avogadro’s Law: equal volumes of different gases at the same P and T contain the same number of molecules.

  21. Boyle’s law: V / P-1 (Constant n, T) Charles’ law: V / T (Constant P,n) Avogadro’s law: V / N (constant P, T) The Ideal-Gas Equation Putting the three laws together:

  22. Ideal Gas Law The combination of these three laws gives the ideal gas law which is a special form of an equation of state, i.e., an equation relating the variables that characterize a gas (pressure, volume, temperature, density, ….). The ideal gas law is applicable to low-density gases.

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