PHYSICS 231 Lecture 23 Temperature PHY 231 1 Pascal s Principle If we exert pressure on any part of an incompressible fluid this pressure will be t transferred f d to t the th restt of f the th fluid fl id with ith no losses l This concept is called Pascal s Principle and can be stated When there is a change in pressure at any point in a confined fluid there is an equal change in pressure at every point in the fluid fluid Pascal s Principle is the basis for many modern hydraulic y devices in use today y PHY 231 2 Pressure at depth h P P0 fluidgh h distance between liquid surface and the point where you measure P P0 h P Buoyantt force B f f for submerged b d object bj t B fluidVobjectg Mfluidg wfluid The buoyant y force equals q the weight g of the amount of water that can be put in the volume taken by the object If object is not moving B wobject object fluid b b fl d Buoyant force for floating object The buoyant force equals the weight of the amount of water that can be put in the part of the volume of the object that is under water objectVobject waterVdisplaced h h objectVobject waterA object fluid PHY 231 B h w 3 Buoyant force For floating object object fluid Vdisplaced Mobject water Mobject objectVobject For submerged object object orr fluid Vdisplaced Vobject Vobject Mobject object PHY 231 4 Bernoulli s equation P1 v12 gy1 P2 v22 gy2 P v2 gy constant The sum of the pressure P P the kinetic energy per unit volume v2 and the potential energy per unit volume gy is constant at all points along a path of flow Note that for an incompressible fluid A1v1 A2v2 This is called the equation of continuity PHY 231 5 quiz A boat carrying a large rock is floating on a lake The rock is thrown overboard and sinks The water level in the lake with respect to the shore rock water a rises b drops rock overboard c remains the same boat rock in boat B Mg B Mg Vdispl Mboat water Vdispl waterg Mboat Mrock g rock under water Vdispl di l Mboat b t Mrock k water t Vrock Mrock rock Mboat water Mrock water Mrock water so lower ow r tota total displaced volume PHY 231 6 Quiz Floating in two different liquids 90 under water Density 0 9 of that of water Now pour paint thinner density 0 0 8 8 of that of water on top Paint thinner does not mix with water What will happen A Cylinder rises B Cylinder sinks C Cylinder remains att same height h i ht PHY 231 7 90 under water Density 0 9 of that of water A Cylinder rises B Cylinder sinks C Cy Cylinder de remains e a s at same height PHY 231 8 Example Bernoulli s Equation We squeeze the bulb of a perfume atomizer causing air to flow horizontally across the opening of of a tube that extends down into the perfume If the air is moving at 50 0 m s what is the pressure difference at the top of the tube v Before we squeze the bulb v0 0 1 2 1 2 p v p0 v0 p0 2 2 1 2 p p0 v 2 1 2 1 30 kg m 3 50 0 m s p p0 v 1630 Pa 2 2 2 PHY 231 9 Quiz When I blow on the straw between the two cans what will happen pp A The cans move apart B The cans move inward C The cans don t move at all PHY 231 10 Quiz An ideal fluid flows through a pipe whose vertical cross section side view is shown At R and S the pipe has diameter 2 cm At Q the pipe has diameter 1 cm Q and S are at the same height The fluid speed at Q is that at R A Greater than B Less than C Equal to PHY 231 11 Quiz An ideal fluid flows through a pipe whose vertical cross section side view is shown At R and S the pipe has diameter 2 cm At Q the pipe has diameter 1 cm Q and S are at the same height The pressure at Q is that at S A Greater than B Less than C Equal to PHY 231 12 Quiz An ideal fluid flows through a pipe whose vertical cross section side view is shown At R and S the pipe has diameter 2 cm At Q the pipe has diameter 1 cm Q and S are at the same height The pressure at R is that at S A Greater than B Less than C Equal to PHY 231 13 Quiz The driver of a car decides to smoke a cigar Which window should be opened so that the passenger sitting beside the driver does not have to breathe the secondhand smoke A The driver side window B The passenger side passenger side window PHY 231 14 Potential Energy Chapter 12 Temperature Kinetic energy T 0 E Emin R The curve depends on the material material e g e g Emin is different for water and iron R 2 atom molecules l l PHY 231 15 Solid low T Potential Energy 0 Ki ti energy T Kinetic Rmin R Emin The temperature and thus kinetic energy is so small that the atoms molecules can only oscillate around a fixed position Rmin PHY 231 16 Potential Energy 0 Liquid medium T Kinetic energy T Rmin R Emin On average the atoms molecules like to stick together but sometimes escape and can travel far far PHY 231 17 Gas high T Potential Energy R min Kinetic energy T 0 Emin R The kinetic energy is much larger than Emin and the atoms molecules move around randomly PHY 231 18 What happens if the temperature of a substance is increased Rmin Rave T 0 Kinetic energy T Rave T 0 Rmin 0 Emin R T 0 Average distance between atoms molecules Rmin T To The average distance between atoms molecules is larger than Rmin i the substance expands 19 PHY 231 Temperature scales Conversions Tcelsius Tkelvin 273 15 Tfahrenheit 9 5 Tcelcius 32 We will use Tkelvin If Tkelvin 0 0 the th atoms molecules t l l have no kinetic energy and every substance is a solid it is called the Absolute zero point Celsius Fahrenheit Kelvin PHY 231 20 Thermal expansion length L L Lo T surface f A A A Ao T T 2 2 volume V V V Vo T 3 3 L0 coefficient of linear expansion different for each material Some examples examples 24E 06 1 K Aluminum 1 2E 04 1 K Alcohol PHY 231 T T0 T T0 T 21 Water a special case Coef of expansion is Coef negative If T drops the volume becomes larger Coef Of expansion is positive i i if T d drops the h volume becomes smaller Ice is formed it floats …
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