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Thermal Physics IB Physics

Thermal Physics IB Physics. Topic 3: Ideal gases. Ideal Gases. Understand and Apply the following. Pressure. Gas Laws (by name) PV = nRT Kinetic Molecular Theory Explain Pressure. WilliamThompson (Lord Kelvin). Pressure. Click on Me. Pressure is defined as force per unit area

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Thermal Physics IB Physics

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  1. Thermal PhysicsIB Physics Topic 3: Ideal gases

  2. Ideal Gases • Understand and Apply the following. • Pressure. • Gas Laws (by name) • PV = nRT • Kinetic Molecular Theory • Explain Pressure WilliamThompson (Lord Kelvin)

  3. Pressure Click on Me • Pressure is defined as force per unit area • Newtons per square metre or N/m2 • 1 Nm-2 = 1 Pa (pascal) • The weight of the person is the force applied to the bed and the small area of each nail tip combines to make an overall large area. • The result is a small enough pressure which does not puncture the person.

  4. Atmospheric Pressure • Basically weight of atmosphere! • Air molecules are colliding with you right now! • Pressure = 1.013 x105 N/m2 = 14.7 lbs/in2! • Example: Sphere w/ r = 0.1 m • Demo A = 4 p r2 = .125 m2 F = 12,000 Newtons (over 2,500 lbs)! 21

  5. Qualitative Demonstration of Pressure • Force due to molecules of fluid colliding with container. • Force αImpulse = Dp • Average Pressure = F / A y 16

  6. Pressure • Pressure is defined as force per unit area • Newtons per square metre N/m2 • The pressure exerted by a gas results from the atoms/ molecules “bumping” into the container walls • More atoms gives more bumps per second and higher pressure • Higher temperature means faster atoms and gives more bumps per second and higher pressure • At sea level and 20°C, normal atmospheric pressure is • 1atm ≈ 1 x 105 N/m2

  7. Gases • Gases (as we will see) can behave near perfectly. • NA= 6.02 x 1023 molecules mol-1 • Molecules size ~ 10-8 m to 10-10 m Example: How molecules are there in 6 grams of hydrogen gas? • We have 3 moles, H2 has 2 grams mol-1 • 3 x 6.02 x 1023 = 1.81 x 1024 molecules.

  8. Example Make a rough estimate of the number of water molecules in an ordinary glass of water. • A glass contains about 0.3 L of water, which has a mass of about 300 g. Since the molar mass of water (H2O) is 18 g mol-1 • Hence, 300g/18g mol-1 ~ 17 mol ~ 1025 molecules

  9. The Boyle-Mariotte Law • Gases (at constant temperature) decrease in volume with increasing pressure. • P =F/A • V = πr2 h

  10. Figure 17-3Increasing Pressure by Decreasing Volume

  11. The Boyle-Mariotte Law • Gases (at constant temperature) decrease in volume with increasing pressure. • Isothermal Process • PV = constant • P1V1 = P2V2

  12. Example • The pressure of gas is 2 atm and its volume 0.9 L if the pressure is increased to 6 atm at constant temperature, what is the new volume? • Answer: P1V1 = P2V2 2 x 0.9 = 6 x V; hence V = 0.3 L

  13. The volume-temperature law • Charles & Gay-Lussac • Isobaric Process • V/T = constant • V1 /T1 = V2 /T2 • At absolute zero a gas would take up zero volume. In reality they liquefy when they get really cold!

  14. The pressure-temperature Law • Gases (at constant volume) increase in temperature with increasing pressure. • Isochoric Process • P/T= constant • P1/T1 = P2/T2 pressure 0 100 -200 -100 200 temp. °C

  15. A bottle of hair spray is filled to a pressure of 1 atm at 20°C What is the canister pressure if it is placed into boiling water, and allowed to reach thermal equilibrium? Example P1/ T1 = P2/ T2 or p1 T2 = p2 T1 1 / 293 = p2 / 373 p2 = 373/293 p2 = 1.27 atm

  16. Absolute zero • Ideal gas has zero volume • Resistance of metal drops to zero (actually superconductivity cuts in above 0K) • Brownian motion ceases!(kinetic energy = 3/2 kT) • But lowest temperature attained is ≈ 10-9K pressure 0 temp. °C -273 °C

  17. Equations of state • State, identifies whether solid liquid or gas • Key parameters or state variables • Volume, V (m3) • Pressure, p (N/m2) • Temperature, T (K) • Mass, M (kg) or number of moles, n • Equation of state relates V, p , T, m or n

  18. Bulk vs molecules • Consider force between two molecules • At absolute zero • No thermal energy • Molecules sit at r0 • Above absolute zero • Some thermal energy • Molecules are at r> r0 (thermal expansion) • At high temperature • Thermal energy > binding energy • Molecules form a gas force energy repulsion r0 r attraction binding energy thermal energy

  19. Equation of state for a gas • All gases behave nearly the same • pV = nRT • R = 8.3 J/(mol K) for all gases (as long as they remain a gas) • T is in K!!!!!!

  20. What is the mass of a cubic metre of air? Molecular weigh of air ≈ 32g Example pV = nRT Atmospheric pressure = 105 N/m2 Atmospheric temp. = 300K For a volume of 1 m3 n = pV/RT = 105 / (8.3 x 300) = 40 moles M = 40 x 0.032 = 1.3kg

  21. Constant mass of gas • For a fixed amount of gas, its mass or number of moles remains the same • pV/T = nR = constant • Comparing the same gas under different conditions • p1V1/T1 = p2V2/T2 • Hence can use pressure of a constant volume of gas to define temperature (works even if gas is impure - since all gases the same) • Must use T in K!!!!!!

  22. A hot air balloon has a volume of 150m3 If heated from 20°C to 60°C how much lighter does it get? Molecular weight of air ≈32g Example pV/T = nR n = pV/RT Balloon has constant volume and constant pressure ncool =105x150 / (8.3 x293) = 61680 nhot =105x150 / (8.3 x333) = 54271 Dn = 7409 moles DM = 7409 x 0.032 = 237kg

  23. Molecules have finite size • Cannot reduce volume of gas to zero! • When you try, it becomes a liquid • Slightly increases the measured volume • Atoms/ molecules always attract each other • Slightly reduces the measured pressure • Van de Waals forces

  24. p-V diagrams (for gases) • Useful to consider the pressure/volume changes at constant temperature • Isotherms are p-V values for a fixed amount of gas at constant volume • p a 1/V Increasing temperature Pressure volume

  25. Kinetic theory of gases • A gas consists of a large number of molecules. • Molecules move randomly with a range of speeds. (Maxwell's Distribution) • The Volume of the molecule is negligible compared with the volume of the gas itself. • Collisions are elastic (KE conserved) • No inter-molecular forces. • Collision time with walls are very smal. • Molecules obey Newton’s Laws of Mechanics

  26. Molecules in a gas • Gas atoms/molecules move in a straight line • velocity due to thermal energy • KE = 1/2 m vx2 ≈ 3/2 kT • KEavgα absolute temp • RMS – (Root mean squared) • Pressure results from collisions with the walls of the container. (NOT collisions between molecules • Fimpact = Δp/t = (2m vx)/t

  27. How fast does a typical gas molecule (travel at room temperature? Lets take Nitrogen-14!(k = 1.38x10-23J/K) Example KE = 1/2 mv2 = 3/2 kT v = (3kT/m)1/2 v = [(3)(1.38x10-23 x 293/(4.65x10-26)]1/2 v = 511 m/sec

  28. If it takes 2 mins for your kettle to begin boiling how much longer does it take to boil dry? Assume kettle is 3kW Starting temp of water 20°C Example Work done by kettle = power x time = 2 x 60 x 3000 = 360 000J = Work to boil water of mass M = DT x M x cwater 360 000J = 80 x M x 4190 Mass of water = 1.07kg Energy to boil water = M x Lv (water) = 1.07 x 2256 x103= 2420 000J Time required = Energy /power = 2420 000/3000 = 808 s ≈ 13mins

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