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Physics Subject Area Test Thermodynamics * There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin. Converting Between the Kelvin and Celsius Scales Converting Between the Fahrenheit and Celsius Scales Thermal expansion • Expanding solids maintain original shape • Expanding liquids conform to the container Linear expansion ΔL = αLΔT L = length α = coefficient of liner expansion ΔT = temperature change Example: The highest tower in the world is the steel radio mast of Warsaw Radio in Poland, which has a height if 646m. How much does its height increase between a cold winter day when the temperature is -35⁰C and a hot summer day when the temperature is +35 ⁰C ? ΔL = αLΔT = 12x10-6/ ⁰C x 646 x 70 ⁰C = 0.54m • Volume expansion ΔV= βVΔT L = length β = coefficient of liner expansion ΔT = temperature change cold Β=3α hot Heat flow: the heat current; the amount of heat that passes by some given place on the rod per unit time ∆ ∆ = heat flow k = proportionality constant, thermal conductivity A = cross sectional area ΔT = change in temperature Δx = distance crossed, thickness of material * convection Heat is stored in a moving fluid and is carried from one place to another by the motion of this fluid * radiation The heat is carried from one place to another by electromagnetic waves * conduction the process of handing on energy from one thing to the next * Amount of power radiated (I) by a body at temperature T and having a surface area A is given by the Stefan-Boltzmann law = 4 I = power radiated e = emissivity (between 0 and 1) σ = Stefan’s constant = 5.6703 x 10-8 W/m2·K A = surface area T = temperature Shiny objects are not good absorbers or radiators & have emissivity close to 0 Black objects have emissivity close to 1 Latent heat ( heat of transformation) – the heat absorbed during the change of state = ∆ ΔQ = quantity of heat transferred m = mass of the material Heat of fusion - heat absorbed when changing from a solid to a liquid Heat of vaporization - heat absorbed when changing from a liquid to a gas GAS LAWS P= pressure V = volume P1V1=P2V2 V1/V2=T1/T2 V = volume T = temperature P1/T1=P2/T2 P = pressure T = temperature Combined Gas Law 1 1 1 = 2 2 2 Ideal Gas Law PV = n R T P= pressure V = volume T = temperature n = moles R = Gas constant = 0.08206 L-atm/mol K *Gas Density PV = nRT n/V = P/RT Molarity = n/V Density D = m/V Molecular Wt M = m/n PM/RT M= DRT/P D=Mn/V = * Energy can be neither created nor destroyed but only transformed THE GENERAL ENERGY EQUATION Energy In = Energy Out or U2 - U1 = Q -W where U1: internal energy of the system at the beginning U2: internal energy of the system at the end Q : net heat flow into the system W : net work done by the system Q = ΔU + ΔW A closed tank has a volume of 40.0 m2 and is filled with air at 25⁰C and 100 kPa. We want to maintain the temperature in the tank at 25⁰C as water is pumped into it. How much heat will have to be removed from the air in the tank to fill it half full? = 1 2 2 = 1 = 1 = 2 = (100kPa) (40.0 m2)(-0.69314) = -2772.58kJ * • Isobaric – the pressure of and on the working fluid is constant – represented by horizontal lines on a graph • Isothermal – temperature is constant – Temperature doesn’t change, internal energy remains constant, & the heat absorbed by the gas = the work done by the gas – The PV curve is a hyperbola • Adiabatic – there is no transfer of heat to or from the system during the process – Work done = decrease in internal energy & the temperature falls as the gas expands – -the PV curve is steeper than that of and isothermal expansion * Quasi-Static Processes Quasi-static (quasi-equilibrium) processes – sufficiently slow processes, any intermediate state can be considered as an equilibrium state (the macroparamers are welldefined for all intermediate states). Advantage: the state of a system that participates in a quasi-equilibrium process can be described with the same (small) number of macro parameters as for a system in equilibrium (e.g., for an ideal gas in quasiequilibrium processes, this could be T and P). By contrast, for nonequilibrium processes (e.g. turbulent flow of gas), we need a huge number of macro parameters. Examples of quasiequilibrium processes: isochoric: isobaric: isothermal: adiabatic: V = const P = const T = const Q=0 For quasi-equilibrium processes, P, V, T are well-defined – the “path” between two states is a continuous lines in the P, V, T space. P T 2 1 V * Work A – the The work done by an external force on a gas enclosed within a cylinder fitted with a piston: piston area W = (PA) dx = P (Adx) = - PdV force x P The sign: if the volume is decreased, W is positive (by compressing gas, we increase its internal energy); if the volume is increased, W is negative (the gas decreases its internal energy by doing some work on the environment). W 1 2 V2 P (T , V ) dV V1 W = - PdV - applies to any shape of system boundary dU = Q – PdV The work is not necessarily associated with the volume changes – e.g., in the Joule’s experiments on determining the “mechanical equivalent of heat”, the system (water) was heated by stirring. *Specific Heat the heat absorbed during the change of state Q = nCv ΔT Q = amount of heat required n = number of moles Cv = specific heat at a constant volume ΔT = Change in temperature How to calculate changes in thermal energy Specific heat is the amount of heat required to raise the temperature of 1 kg of a material by one degree (C or K). C water = 4184 J / kg C Q = m x T x Cp Q = change in thermal energy m = mass of substance T = change in temperature (Tf – Ti) Cp = specific heat of substance Second Law of Thermodynamics Entropy = the transformation of energy to a more disordered state - can be thought of as a measure of the randomness of a system - related to the various modes of motion in molecules The second law of thermodynamics: entropy of an isolated system not in equilibrium tends to increase over time • No machine is 100% efficient • Heat cannot spontaneously pass from a colder to a hotter object The relationship between kinetic energy and intermolecular forces determines whether a collection of molecules will be a solid, liquid or a gas * Pressure results from collisions * The # of collisions and the KE contribute to pressure * Temperature increase KE