# A Brief History of Planetary Science - Augustana College

Review for Final Physics 313 Professor Lee Carkner Lecture 25 Final Exam Final is Tuesday, May 18, 9am 75 minutes worth of chapters 9-12 45 minutes worth of chapters 1-8 Same format as other tests (multiple

choice and short answer) Worth 20% of grade Three formula sheets given on test (one for Ch 9-12 and previous two) Bring pencil and calculator Exercise #24 Maxwell Set escape velocity equal to maximum

Maxwell velocity (2GM/R) = 10(3kT/m) m = (150KTR/GM) Planetary atmospheres Earth: m > 9.5X10-27 kg (NH3, O2) Jupiter: m > 1.4X10-28 kg (He, NH3, O2) Titan: m > 5.6X10-26 kg (None) Moon: m > 2.2X10-25 kg (None) Thermal Equilibrium Two identical metal blocks, one at 100 C

and one at 120 C, are placed together. Which transfers the most heat? Two objects at different temperatures will exchange heat until they are at the same temperature Zeroth Law: Two systems in thermal equilibrium with a third are in thermal equilibrium with each other Heat Transfer Heat: Q = mcT = mc(Tf-Ti)

Conduction: dQ/dt = -KA(dT/dx) Q/t = -KA(T1-T2)/x Radiation dQ/dt = A(Tenv4-T4) Temperature How would you make a tube of mercury into a Celsius thermometer? A Kelvin thermometer? Thermometers defined by the triple point of water

A system at constant temperature can have a range of values for the other variables Isotherm Measuring Temperature Thermometers T (X) = 273.16 (X/XTP) Temperature scales T (R) = T (F) + 459.67 T (K) = T (C) + 273.15 T (R) = (9/5) T (K)

T (F) = (9/5) T (C) +32 Equations of State If the temperature of an ideal gas is doubled while the volume stays the same, what happens to the pressure? Equation of state detail how properties change with temperature Increasing T will generally increase the force and displacement terms Mathematical Relations

General Relations: dx = ( x/y)zdy + (x/z)ydz (x/y)z = 1/(y/x)z (x/y)z(y/z)x(z/x)y = -1 Specific Relations: Volume Expansivity: = (1/V)(dV/dT)P Isothermal Compressibility: =-(1/V)(dV/dP)T

Linear Expansivity: = (1/L)(dL/dT) Youngs modulus: Y = (L/A)(d/dL)T Work How much work is done in an isobaric compression of a gas at 1 Pa from 2 to 1 m3? The work done a system is the product of a force term and a displacement term No displacement, no work Compression is positive, expansion is

negative Work is area under PV (or XY) curve Work is path dependant Calculating Work dW = -PdV W = - PdV For ideal gas P = nRT/V Examples: Isothermal ideal gas: W = -nRT (1/V) dV = -nRT ln (Vf/Vi) Isobaric ideal gas:

W = -P dV = -P(Vf-Vi) First Law Rank the following processes in order of increasing internal energy: Adiabatic compression Isothermal expansion Isochoric cooling Energy is conserved Internal energy is a state function, work and heat are not

First Law Equations U = Uf-Ui = Q+W dU = dQ +dW dU = CdT - PdV Ideal Gas If the volume of an ideal gas is doubled and the pressure is tripled isothermally, how does the internal energy change? lim (PV) = nRT (dU/dP)T = (dU/dV)T = 0

(dU/dT)V = CV CP = CV + nR dQ = CVdT+PdV = CPdT-VdP Adiabatic Processes Can an adiabatic process keep constant P, V, or T? PV = const TV-1 = const T/P(-1)/= const W = (PfVf - PiVi)/-1

Kinetic Theory If the rms velocity of gas molecules doubles what happens to the temperature and internal energy (1/2)mv2 = (3/2)kT U = (3/2)NkT T = mv2/3k Engines If the heat entering an engine is doubled and the work stays the same

what happens to the efficiency? Engines are cycles Change in internal energy is zero Composed of 4 processes = W/QH = (QH-QL)/QH = 1 - QL/QH QH = W + Q L Types of Engines Otto Adiabatic, Isochoric = 1 - (T1/T2)

Diesel Adiabatic, isochoric, isobaric = 1 - (1/)(T4-T1)/(T3-T2) Rankine (steam) Adiabatic, isobaric Stirling Isothermal, isochoric Refrigerators Transfer heat from low to high T with

the addition of work Operates in cycle Transfers heat with evaporation and condensation at different pressures K = QL/W K = QL/(QH-QL) Second Law Is an ice cube melting at room temperature a reversible process? Kelvin-Planck Cannot convert heat completely into

work Clausius Cannot move heat from low to high temperature without work Carnot What two processes make up a Carnot cycle? How many temperatures is heat transferred at? Adiabatic and isothermal = 1 - TL/TH

Most efficient cycle Efficiency depends only on the temperature Second Law The second law of thermodynamics can be stated: Engine cannot turn heat completely into work Heat cannot move from low to high temperatures without work Efficiency cannot exceed Carnot efficiency

Entropy always increases Entropy Entropy change is zero for all reversible processes All real processes are irreversible Can compute entropy for an irreversible process by replacing it with a reversible process that achieves the same result Entropy change of system + entropy

change of surroundings = entropy change of universe (which is > 0) Determining Entropy Can integrate dS to find S dS = dQ/T S = dQ/T (integrated from Ti to Tf) Examples: Heat reservoir (or isothermal process) S = Q/T Isobaric S = CP ln (Tf/Ti)

Pure Substances Can plot phases and phase boundaries on a PV, PT and PTV diagram Saturation condition where substance can change phase Critical point above which substance can only be gas where (P/V) =0 and (2P/V2) = 0 Triple point

where fusion, sublimation and vaporization curves intersect Properties of Pure Substances c = (dQ/dT) (per mole) P P cV = (dQ/dT)T (per mole) = (1/V)(dV/dT)P

= -(1/V)(dV/dP)T cP, cV and are 0 at 0 K and rise sharply to the Debye temperature and then level off cP and cV end up near the Dulong and Petit value of 3R is constant at a finite value at low T and then increases linearly Characteristic Functions and Maxwells Relations Legendre Transform: df = udx +vdy

g= f-ux dg = -xdu+vdy Useful theorems: (x/y)z(y/z)x(z/x)y=-1 (x/y)f(y/z)f(z/x)f=1 dU = -PdV +T dS dH = VdP +TdS dA = - SdT - PdV dG = V dP - S dT (T/V)S = - (P/S)V (T/P)S = (V/S)P

(S/V)T = (P/T)V (S/P)T = -(V/T)P Key Equations Entropy T dS = CV dT + T (P/T)V dV T dS = CP dT - T(V/T)P dP Internal Energy (U/V)T = T (P/T)V - P (U/P)T = -T (V/T)P - P(V/P)T Heat Capacity CP - CV = -T(V/T)P2 (P/V)T

cP - cV = Tv2/ Joule-Thomson Expansion Can plot on PT diagram Isenthalpic curves show possible final states for an initial state = (1/cP)[T(dv/dT)T(dv/dT)P - v] = slope Inversion curve separates heating and cooling region =0

Total enthalpy before and after throttling is the same For liquefaction: hi = yhL + (1-y)hf Clausius-Clapeyron Equation Any first order phase change obeys: (dP/dT) = (sf -si)/(vf - vi) = (hf - hi)/T (vf -vi) dP/dT is slope of phase boundary in PT diagram

Can change dP/dT to P/T for small changes in P and T Open Systems For a steady flow open systems mass and energy are conserved: min = mout in [T(dv/dT)Q + W + m] = out [T(dv/dT)Q + W + m] Where is energy per unit mass or: = h + ke +pe (per unit mass) Chemical potential = = (U/n) i = f

For open systems in equilibrium:

## Recently Viewed Presentations

• Our At Aetna, we put the people who use our services at the center of everything we do, and we live by a core set of values. From innovative technology…to building trusting relationships…to honoring our commitments, Aetna takes our core...
• Competitive Dynamics: 3 Market Cycles (Cont'd) 2. Fast-Cycle Markets. Markets in which the firm's capabilities that contribute to competitive advantages are not shielded from imitation and where imitation is often rapid and inexpensive
• An active shooter's overriding objective appears to be that of mass murder, rather than criminal conduct such as robbery, kidnapping, etc." - NTOA ACTIVE SHOOTER RESPONSE Texas Tower - 1966 - resolved by patrol - created need for SWAT.
• Importance of Text in a Multimedia Presentation. Words and symbols in any form, spoken or written, are the most common means of communication. Text is a vital element of multimedia menus, navigation systems, and content.
• Situación Actual de la Epidemia de Influenza A H1N1 Situación Actual de la Epidemia de Influenza A H1N1 Mitos * Virus ADN ARN Herpesviridae Adenoviridae Papovaviridae Hepadnaviridae Poxviridae Parvoviridae Picornaviridae Caliciviridae Paramyxoviridae Orthomyxoviridae Rhabdoviridae Filoviridae Bornaviridae Retroviridae Togaviridae Flaviviridae ...
• LED, photodetectors and solar cell The light emitting diode Materials for LEDs Materials for visible wavelength LEDs Junction photodetectors Photoconductor Photoconductive gain analysis Solar cell Core Book; Introductory Semiconductor Device Physics by Greg PARKER OBJECTIVES At the end of the...
• Seminole Indians of the Southeast Climate & Region Southeastern part of the United States Originally in present-day Florida Forced to move up to Everglades and eventually to Oklahoma Warm climate chickee wigwams What did you observe about the food, clothing,...
• Early Stage Small Business Investment Companies. January 2013. This overview provides some insight into the financial health of the SBIC program. It includes the following: Financial Exposure. Leverage by Capital Impairment. Transfers to the Office of Liquidation. Recovery Rates. Underlying...