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Paperwork

Paperwork. Mastering Physics Course # DRKIDD880131 Assignments should be up Need to be de-enrolled from Physics I. Schedule Short Term. Today – Equations for #2? Monday – Off Tuesday – Lab #1 Copyworks Quiz#1 [Chapter 17] Wed HMWK due 11pm Finish Chapter 18. Equation of State.

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Paperwork

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  1. Paperwork • Mastering Physics • Course # DRKIDD880131 • Assignments should be up • Need to be de-enrolled from Physics I

  2. Schedule Short Term • Today – Equations for #2? • Monday – Off • Tuesday – Lab #1 • Copyworks • Quiz#1 [Chapter 17] • Wed HMWK due 11pm • Finish Chapter 18

  3. Equation of State • Relationship between • p, pressure • V, volume • T, temperature • m or n (mass or # moles) • Related by Molar Mass (MM)

  4. Equation of State • Relationship between • p, pressure • V, volume • T, temperature • m or n (mass or # moles) • Related by Molar Mass (MM)

  5. Equation of State for Solid • Volume • Related to mass & density • V = m/r • For a given volume V0: • Relate to changes in temperature & pressure • V = V0 [ 1+b(T-T0) – k(p-p0) ] • Examine this equation for a solid • If T = T0 & p = p0? • What happens if T not T0, p not p0?

  6. Equation of State for Gas • pV=nRT • Identify Equation components • Units of pV? • “Better” Version • pV = NkBT • kBT = Thermal Energy, more “Physicsy” • Notice

  7. Gas Density at given Parameters • pV=nRT • r = m/V • m = nM (M is Molar Mass) • Algebra to isolate m/V • n = m/M • pV = (m/M)RT • pV/(RT) = m/M • pM/(RT) = m/V = r • Gas density equation. Examine

  8. Gas Density at given Parameters • pV=nRT • r = m/V • m = nM (M is Molar Mass) • Algebra to isolate m/V • n = m/M • pV = (m/M)RT • pV/(RT) = m/M • pM/(RT) = m/V = r • Gas density equation. Examine • density is amount of mass per unit volume (dm/dV)

  9. Isolated SystempV=nRT • Examine a closed system • Mass cannot enter or escape • Balloon? Gas Tank? • Examine at different parameters • p,V,T can change. R & n constant • p1V1/T1 = nR : case 1 • p2V2/T2 = nR : case 2 • Example, what happens to a balloon that gets hot?

  10. Isolated SystempV=nRT • p1V1/T1 = nR : case 1 • p2V2/T2 = nR : case 2 • Example, what happens to a balloon that gets hot? • What is pressure felt by balloon? • Warm balloon by some method. • Does pressure change? • What happens to balloon? • Approximation for weak rubber casing.

  11. Pressure vs. Height • Example 18.4 Force = pA + (dp)A dy Thin object, mass m Force = pA For an object in a fluid Pressure on sides of object is the same, so cancels (Book on desk is stationary) Assume pressure felt by top is slightly different than bottom (p+dp)

  12. Pressure vs. Height • Example 18.4 Force = pA + (dp)A dy Thin object, mass m Force = pA For an object in a fluid Pressure on sides of object is the same, so cancels (Book on desk is stationary) Assume pressure felt by top is slightly different than bottom (p+dp) dp can be +, - or even zero. Just much smaller than p for thin object Let’s say this object is stationary – floating in the fluid. What is sum of all forces on object? What are all forces on object? What if “Object” was just a portion of the fluid itself?

  13. Pressure vs. Height • Example 18.4 Force = pA + (dp)A dy mass = rV = rA(dy) Force = pA SF = 0 = pA - [pA + (dp)A] – mg 0 = pA – pA – (dp)A – rVg (dp)A = -rVg (dp)A = -r(Ady)g (dp/dy) = - rg Implications?

  14. Pressure vs. Height • Example 18.4 Force = pA + (dp)A dy mass = rV = rA(dy) Force = pA SF = 0 = pA - [pA + (dp)A] – mg 0 = pA – pA – (dp)A – rVg (dp)A = -rVg (dp)A = -r(Ady)g (dp/dy) = - rg For Ideal Gas r = m/V = pM/(RT) (dp/dy) = - rg

  15. Pressure vs. Height • Example 18.4 Force = pA + (dp)A dy mass = rV = rA(dy) Force = pA Pressure vs. Height Any Fluid (dp/dy) = - rg For Fluid that is an Ideal Gas r = m/V = pM/(RT) (dp/dy) = - pgM/(RT)

  16. Pressure vs. Height • (dp/dy) = - pgM/(RT) • Now need to set up equation to solve • (dp/p) = -(gM/RT)(dy) • Assume a constant temperature (?)

  17. Pressure vs. Height • (dp/dy) = - pgM/(RT) • Now need to set up equation to solve • (dp/p) = -(gM/RT)(dy) • Assume a constant temperature (?)

  18. Pressure vs. Height

  19. Pressure vs. Height Let’s say integration was from sea level (p0=p0, y0 = 0) To a point pF = p, yF = y Need to have known endpoints Then can derive equation for air pressure as a function of height above sea level Happy Equation: Should Check Accuracy Implications? Check at sea level.

  20. Schedule Short Term • Today – Equations for #2? • Monday – Off • Tuesday – Lab #1 • Copyworks • Quiz#1 [Chapter 17] • Wed HMWK due 11pm • Finish Chapter 18

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