PHY1039 Properties of Matter Heat Capacity of Ideal

PHY1039 Properties of Matter Heat Capacity of Ideal

PHY1039 Properties of Matter Heat Capacity of Ideal Gases (CP and CV) and Adiabatic Expansion of Ideal Gas (See Finns Thermal Physics, Ch. 4) March 12 and 15, 2012 Lectures 11 and 12 From next week: Lectures on Monday at 3 pm will meet in Lecture Theatre E. Week 7 (next week) only: Lecture on Monday, March 19 at 4 pm in 35AC04 (instead of tutorial) Tutorial will be held on Thursday, March 22 at 9 am in the Austin Pearce Building, Lab2 (AP Lab2) Two Types of Heat Capacity

Isochoric Process: CV P P2 T2 (V1, P2) Isobaric Process, CP P P1 T1 T2 (V1, P1) P1 T1

(V2, P1) (V1, P1) V1 T2 > T1 V V1 V2 T2 > T1 V Internal Energy, U, of Monoatomic Gas Monoatomic gases have one atom per molecule: e.g. He, Ne, Xe, and Kr.

All of the kinetic energy of a monoatomic gas is contained in translational motion with a velocity n. nz n There are three degrees of freedom. Each d.o.f. has kT in thermal energy. k = 1.38 x 10-23 J/K The total energy of each molecule (ignoring potential energy) is . ny nx

Translational energy KE = = Ideal Gas Internal Energy, U, of Diatomic Gas Diatomic gases have two atoms per molecule: e.g. H2, O2, N2, CO, Cl2. Diatomic molecules have translational, rotational and vibrational energy: Three translational degrees of freedom: nx, ny, nz Three rotational degrees of freedom: about x, y and z axes. Figure from Understanding Properties of Matter by M. de Podesta But the energy of rotation about the molecules axis is not accessible

at lower temperatures. Internal Energy, U, of Diatomic Gas Diatomic molecules can also have vibrational energy, but it is not accessible at lower T. (Kinetic energy and potential energy of vibration each contribute one d.o.f.) Inaccessible states r N N PE = K (r ro)2 Accessible state There are five degrees of freedom accessible at lower temperatures.

The total energy of each molecule (ignoring potential energy) is 5(1/2)kT = (5/2)kT at lower T, but it will increase with T. Internal Energy, U, of Triatomic Gas Linear triatomic gases have three atoms per molecule that all lie along the same axis: e.g. CO2. O=C=O Like a diatomic molecule, a linear triatomic molecule has three translational and only two accessible rotational degrees of freedom. A linear molecule with N atoms has 3N-5 modes of vibration. There are two degrees of freedom for vibrational energy accessible at lower temperatures. At lower temperatures, in total there are seven accessible degrees of freedom.

Symmetric & anti-symmetric stretching vibration The total energy of each molecule is 7(1/2)kT = (7/2)kT Bending vibration Internal Energy, U, of Triatomic Gas Non-linear triatomic gases have three atoms per molecule that do not lie along the same axis: e.g. N2O; SO2; H2O For a non-linear triatomic molecule, there are rotations about three axes at lower T: three rotational degrees of freedom. A non-linear molecule with N atoms has 3N-6 modes of vibration. A non-linear triatomic molecule has three degrees of freedom. Figure from P. Atkins The Elements of Physical Chemistry

In total, there are 9 possible degrees of freedom (3 translational, 3 rotational, and three vibrational), but only 7 are accessible at lower temperatures. The total energy of each molecule is 7(1/2)kT = (7/2)kT Greenhouse Effect: A Problem of Thermodynamics http://www.dailymail.co.uk/sciencetech/article-483191/Arctic-ice-cap-melts-smallest-size.html http://jcwinnie.biz/wordpress/?p=2235 Earth can be treated as a thermodynamic system. Why Do Water and Carbon Dioxide Block Thermal Radiation from Earth? Most Intense Thermal Radiation from Earth The resonant frequency of

molecular vibrations is in the same frequency as infrared radiation. http://en.wikipedia.org/wiki/File:Atmosfaerisk_spredning.gif Thermal radiation transmitted through atmosphere to Earth from Sun Wavelength (mm) Thermal radiation from colder Earth transmitted through atmosphere en.wikipedia.org/wiki/User:Dragons_flight/Images Heat Capacity of Ideal Gases

Accessible d.o.f. at lower T Type of Gas Monoatomic 3 3/2 nRT Internal Energy, U Cv 3/2 nR Diatomic 5

5/2 nRT 5/2 nR Triatomic 7 7/2 nRT 7/2 nR U for ideal gases (ignoring potential energy) depends only on T. Cv depends only on the amount of gas (through n). Important Conclusions Isothermal processes: U of an ideal gas is a function of T only. If the temperature is constant (DT = 0), then internal energy is constant: DU = 0. Changes in P and V

will not affect U. First Law tells us: DU = 0 = Q + W So, W = - Q. If there is isothermal work on an ideal gas (W is positive), then heat must go out of the gas. Adiabatic processes: In an adiabatic process, Q = 0. First Law tells us: DU = 0 + W.

If work is done on an ideal gas, such as by compression, W is positive, and hence DU is positive. As DU is proportional to nRDT, the temperature of the gas will also increase. Molar Heat Capacity, CP, of Monoatomic Gas CP = 3/2 nR + nR = 5/2 nR Figure from Understanding Properties of Matter by M. de Podesta At higher temperatures, more degrees of freedom are not excited. There is no T dependence of CV or CP. Molar Heat Capacity, CP, of Diatomic Gas CP = 5/2 nR + nR = 7/2 nR Figure from Understanding Properties of Matter by M. de Podesta

As temperature is increased from room temperature, more degrees of freedom are accessible (rotational and vibrational) Molar Heat Capacities of Various Gases at 25 C From Tiplers Physics Adiabatic versus Isothermal Expansions (or Compressions) of an Ideal Gas P Adiabatic compression: P2 P1 Isothermal compression: = 1

V2 1 V1 V

Recently Viewed Presentations

  • 13 Colonies - Polk County School District

    13 Colonies - Polk County School District

    Southern Colonies. Climate and Physical Features. Great Soil. Warm Weather. Very long growing seasons. Bad harbors. Southern Colonies. Economic Comparative Advantage. Focused on farming cash crops. Large plantation farms for tobacco, cotton, and indigo.
  • Accidents Thermiques

    Accidents Thermiques

    ACCIDENTS THERMIQUES Cpl MAROILLEY Clément CI CHATEAUVILLAIN(52) « BACKDRAFT, RULL OVER, FLASH OVER » Ce sont les trois situations évolutives les plus dangereuses que tout pompiers peut rencontrer sur interventions.
  • Presentation: Program Overview

    Presentation: Program Overview

    Standardization, independent checks, and learning from defects are the principles of safe design. Principles of safe design apply to both technical and team work. Teams with diverse and independent input make wise decisions. 2. Vincent C, Taylor-Adams S, Stanhope N....
  • Texas Board of Occupational Therapy Examiners

    Texas Board of Occupational Therapy Examiners

    Review the licensure application and renewal process and general Board information. ... administrative governmental agency that directly supports or carries out the functions of one or both of the Texas Board of Occupational Therapy Examiners and the Texas Board of...
  • Spinal Cord Repair using Polymeric Substrates

    Spinal Cord Repair using Polymeric Substrates

    a Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, St Lucia, QLD 4072, Australia. b . School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia. c . Division of Molecular Pharmaceutics, Eshelman
  • EUCAS Poster 2005 - Open Research Online

    EUCAS Poster 2005 - Open Research Online

    This is consistent with a drawing process as described in the patent of William Collins. In contrast the bolt from the HMS Impregnable showed lower retained deformation levels and a more complex texture indicating a stronger contribution of recrystallisation.
  • Virus - LACOE

    Virus - LACOE

    Rhinovirus (common cold); poliovirus, hepatitis A virus, and other enteric (intestinal) viruses. Coronavirus. Yes. ... The RNA molecules function both as mRNA for synthesis of viral proteins and as genomes for new virus particles released from the cell.
  • Spring 2015 California Alternate Assessments (CAA) Field Test for

    Spring 2015 California Alternate Assessments (CAA) Field Test for

    In TOMS, select "Paper test assignments" from the "Students" menu ... If the outcome is " ... As a security measure, test sessions are automatically logged off after 30 minutes of test inactivity. This timeout also results in the test...