1 / 19

Entropy

Entropy. Thermodynamics Professor Lee Carkner Lecture 13. PAL # 12 Carnot. Engine powering a heat pump Find work needed for heat pump COP HP = 1 /(1-T L /T H ) = 1/(1 – 275/295) = COP HP = Q H /W in W = Q/COP = 62000/14.75 = Total engine work is twice that needed for heat pump

stevie
Télécharger la présentation

Entropy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Entropy Thermodynamics Professor Lee Carkner Lecture 13

  2. PAL # 12 Carnot • Engine powering a heat pump • Find work needed for heat pump • COPHP = 1 /(1-TL/TH) = 1/(1 – 275/295) = • COPHP = QH/Win • W = Q/COP = 62000/14.75 = • Total engine work is twice that needed for heat pump • Wengine = 2WHP = • hth = 1 – (TL/TH) = 1 – (293/1073) = 0.727 • hth = W/QH • QH = W/hth = 8406/0.727 =

  3. Clausius Inequality ∫ dQ/T = 0 ∫ dQ/T ≤ 0 • Valid for all cycles

  4. Entropy • The integral is a state quantity called the entropy Ds = ∫ dQ/T • Entropy is a tabulated property of a system like v, h or u DS = Q/T

  5. TS Diagram • Can plot a Temperature-Entropy Diagram • The total heat is the integral of TdS, or the area under the process line on a TS diagram • Similar to W being the area in a Pv diagram

  6. Area Under TS Diagram

  7. Mollier Diagram • The vertical (enthalpy) distance gives a measure of the work • The horizontal (entropy) distance gives a measure of the irreversibilities (and thus inefficiencies)

  8. Information From an hs Diagram

  9. Entropy Rules • Processes must proceed in the direction that increases entropy • Entropy is not conserved • Rate of entropy generations tells us the degree of irreversibility and thus efficiency

  10. Finding Entropy Change • Entropy in tables assign zero to some arbitrary point • For mixtures of vapor and liquid: • We will normally assume the entropy of a compressed liquid is the same as a saturated liquid

  11. Entropy of a Pure Substance

  12. Isentropic Process • e.g. well-insulated and frictionless • Can use to determine the properties of the initial and final states of the system • Find s for state 1 and you know that state 2 must have a P and T to give the same s

  13. Isentropic Diagram

  14. Disorder • The higher the entropy the more random the distribution of molecules • High entropy → high disorder → low quality → low efficiency

  15. The 3rd Law • Molecule motions decrease with decreasing temperature • Only one configuration means absolute order

  16. Gibbs Equation • but we already have relationships for Q • Solving for Tds TdS – PdV = dU • Called the Gibbs equation • Substituting into the Gibbs equation: Tds = dh - vdP

  17. Entropy Relations • We can know write integrable equations ds = dh/T + vdP/T • We still need: • e.g., du = cvdT • e.g., Pv = RT

  18. Incompressible Entropy • For solids and liquids the volume does not change much • dv = 0 • We can integrate the entropy equation: DS = ∫ c dT/T = c ln T2/T1

  19. Next Time • Read: 7.7-7.13 • Homework: Ch 7, P: 46, 54, 66, 93

More Related