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First Law of Thermodynamics

First Law of Thermodynamics. Physics 313 Professor Lee Carkner Lecture 8. Exercise #6 Spring. Work done on spring W =  F dx =  kx dx = ½kx 2 = ½k(x 2 2 –x 1 2 ) If the spring is initially unstretched, x 1 = 0 Spring and gas work displacement of spring D V = A D X

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First Law of Thermodynamics

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  1. First Law of Thermodynamics Physics 313 Professor Lee Carkner Lecture 8

  2. Exercise #6 Spring • Work done on spring • W =  F dx =  kx dx = ½kx2 = ½k(x22 –x12) • If the spring is initially unstretched, x1 = 0 • Spring and gas work • displacement of spring DV = A DX • 0.025 = 0.25 Dx, Dx = 0.1 m, x2 = 0.1 m • W = ½kx22 = (½)(150)(0.1)2 = • P = W/DV = 0.75/0.025 = 30 kPa • PV = nRT • T = PV/nR = (30000)(0.025)/(1)(8.31) =

  3. Heat • What is heat? • Heat is not a state variable • No heat transfer if: • Heat is energy and can occur with different processes

  4. Isochoric Heat • If heat is added the temperature of the system will rise • Any heat exchange directly affects the internal energy

  5. Adiabatic Work • In an adiabatic system no heat can flow • For any adiabatic process by which the system move from state 1 to state 2 the total amount of work is a constant • This is not normally true • This work changes the internal energy

  6. Internal Energy • When heat flows into the system or work is done on a system the system gains energy • The internal energy is a property of a system and can be expressed in terms of thermodynamic coordinates • We will often discuss a change in internal energy (DU or dU)

  7. First Law of Thermodynamics • Energy is conserved • Can write in differential form as • dU is a change in internal energy • dQ and dW are small amounts of heat or work

  8. Notes on the First Law • Heat is defined thermodynamically by the first law: • Can also write for work: • Sign Convention • Heat into a system is positive • Work done on the system is positive • This convention can be changed but the first law then also must be changed

  9. Notes on Heat • Heat was once thought to be a fluid within a body • People began to suspect that heat was a form of energy in the early 1800’s, but couldn’t prove it • Joule demonstrated the equivalence of heat and work in the 1840’s

  10. Special Cases • Adiabatic: DU = W • Isochoric: DU = Q

  11. Heat and Internal Energy • If a Styrofoam block and a steel block are both heated the same amount which is hotter? • Why? Q = C DT

  12. Specific Heat • We will also use the heat capacity per mole: • Where n is number of moles or (m/M) total mass divided by molar mass

  13. Heat Capacities • We can express the heat capacity in terms of differential changes in temperature and heat C = dQ/dT • We can then define two specific quantities: CV = (dQ/dT)V CP = (dQ/dT)P • Note that C is a function of temperature

  14. Internal Energy • We can write the heat flow into a system as: • For an isochoric system • So: • The change in internal energy is a function of the change in temperature

  15. Heat Conservation • All objects within the boundary will exchange heat until they are in thermodynamic equilibrium (equal T) • Lost to surroundings

  16. Calorimetry • A calorimeter must : • produce a well defined amount of heat • Monitor temperature • Heat produced must all go into raising temperature of sample

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