Physics THERMAL PHYSICS/EXPANSION. Mr Rishi Gopie

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1 THERMAL PHYSICS/EXPANSION Mr Rishi Gopie

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3 Changes in Size Generally, when heat is added to a body/system it undergoes expansion, i.e. an increase in size, and when heat is removed from the body/system it undergoes contraction, i.e. a decrease in size. Note that a body/system expands/contracts in all directions. a) Expansion/Contraction of solids Allowances must be made for the expansion/contraction of materials used in the construction of roads, buildings, bridges, floors, railway lines, etc. these allowances involve leaving room for the materials to move during expansion/contraction. So that forces will not be set up within them that could cause buckling, bending, cracking and general weakening of structures. Expansion/contraction must also be catered for in dentistry (eg. The use of appropriate filling material), in the removal of metal covers from glass jars/bottles, in the use of steel to reinforce concrete and in using thick/thin glass containers for holding hot fluids. Expansion /contraction is also usefully applied in instruments such as thermostat (i.e. a device for regulating temperature) and a certain type of thermometer (an instrument for measuring temperature). The thermostat and the (certain type of) thermometer make use of a bimetallic strip which is a compound bar consisting of two bars of metal of identical dimensions but different materials that are joined together. The bimetallic strip operates on the principle that different materials expand/contract by different amounts even when heated/cooled by the same amount. Thus when such a strip is heated/cooled, in order to accommodate for one of the material`s expanding/contracting more than the other, the whole strip bends- one way for heating and the opposite way for cooling. Consider the following: If material A expands /contracts more than material B, (i.e. A has a higher thermal expansivity than B) then : 3

4 Diag 16 Such a device is useful in fire alarm circuits for instance Diag 17 b) Expansion/Contraction of liquids. Generally, gases expand/contract more than liquids and liquids expand/contract more than solids. Since liquids (like gases) must be held in some container then the expansion/contraction of the container itself must sometimes also be considered. 4

5 Consider the following situations 1. Heating a liquid in a long necked container consider the effect on the level of the liquid, the long, narrow neck of the container if the container is made of a poor thermal conductor, such as glass, or a good thermal conductor such as a metal. 2. Heating/Cooling a system consisting of a block of solid(s) freely suspended in a liquid (l): Diag The anomalous expansion/contraction of water due to the water having a maximum density at 4 C c) Expansion/Contraction of gases. The Gas laws. Since liquids and solids are considered to be incompressible, pressure is not a factor for them when considering expansion/contraction with changes in temperature. Gases, however, are very much compressible and so pressure is a factor in addition to volume and temperature. The gas laws represent the relationships between pressure (p) and volume (v) and thermodynamic temperature (T) for an ideal gas. They are : 1. Boyle`s law: The pressure of a fixed mass of gas at constant temperature is inversely proportional to its volume. So p 1/v pv = k, (a constant) p1 x v1 = p2 x v2 (T constant) 2. Charles law The volume of a fixed mass of gas at constant pressure is directly proportional to its thermometric temperature: So v T v/t = k2 ( a constant) v1/t1 = v2/t2 (P constant) 5

6 3. Pressure Law The pressure of a fixed mass of gas at constant volume is directly proportional to its thermodynamic temperature. So P α T ð ð P/T = k3 ( a constant) P1/T1 = P2/T2 (V constant) 4. The Universal Gas Law For a fixed mass of gas PV/T = k4 (a constant) ð P1V1/T1 = P2V2/T2 Note that in all the formulae P is the absolute pressure of the gas, i.e. P = Guage Pressure + A.P. T is the thermodynamic temperature of the gas, i.e TK = θ C Consider experiments to investigate the relationship between P,V, and T: 1) Boyle`s law to investigate the relationship between P and V with T constant 6

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8 v is represented by the length l (Shorter leg with scale), of the gas column (since v = A x l and the area of the cross section A, of the tube is constant. so V l ) P is given by : P = h + A.P (or hρg + A.P.). Also P = reading on Bourdon guage (which includes A.P) The values of V ( as represented by l) and P are tabulated: P V 1/V P x V P1 V1 1/V1 K1 P2 V2 1/V2 K2 P3 V3 1/V3 K3 P4 V4 1/V4 K4 P5 V5 1/V5 K5 The last Column ( P x V) gives a constant value (i.e. k1) thus supporting Boyle`s las i.e. p x v = k1, a constant then p = k1/v => p 1/v as Boyle`s law suggests. In addition, graphs of P vs V and P vs 1/v can be plotted and drawn 8

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10 Both graphs show that p 1/v and therefore that p x v = a constant thus supporting Boyle`s law. It is ensured that T remains constant by carrying out the changes in P and V very slowly. 10

11 2) Charles` law to investigate the relationship between V and T at constant P v is represented by the length, l of the gas column (since, once again, v t) T is the temperature reading on the thermometer ( in C) The values of V ( as represented by l) and t are tabulated: 11

12 V t/ C T/K V/T V1 t1 T1 K2 V2 t2 T2 K2 V3 t3 T3 K2 V4 t4 T4 K2 V5 t5 T5 K2 The last column (V/T) gives a constant value (i.e. k2) thus supporting Charles` law (i.e. if V/T = k2, a constant then V = k2t => V T, as Charles` law suggest) In addition graphs of V vs t and V vs T can be drawn 12

13 The graph V vs T shows that V T ( and therefore that V/T = a constant) thus supporting Charles` law. 13

14 3) the Pressure law to investigate the relationship between P and T at constant V 14

15 P is given by p = h + A.P ( or hρg + A.P). Also P = reading on Bourdon guage ( which includes A.P.) t is the reading on the thermometer ( in C) The values od P and t are tabulated: P t/ C T/K P/T P1 t1 T1 K3 P2 t2 T2 K3 P3 t3 T3 K3 P4 t4 T4 K3 P5 t5 T5 K3 The last coulumn (P/T) gives a constant value (i.e. k3) thus supporting the pressure law. (i.e. if P/T = k3, a constant the P = k3t => P T as the pressure law suggests). 15

16 In addition, graphs of p vs t and P vs T can be drawn. the graph of p vs T shows that P T ( and therefore that P/T = a constant) thus supporting the pressure law. Note that for the v- t and p- t graphs, associated with Charles` law and the pressure law respectively, if 273 is added to each t value then the V-T and P-T graphs shown are obtained. These graphs show that v T and P T respectively and encouraged. loed kelvin to propose a temperature scale which started with zero as the lowest possible temperature (i.e. absolute zero) at this temperature (about C) molecules have their minimum amount of energy. The scale he devised is known as the thermodynamic scale or kelvin scale of temperature and indicates a direct relationship between certain properties (such as the pressure and volume of a gas) and thermodynamic temperature. The thermodynamic scale is an example 16

17 of an absolute temperature scale since it does not depend on the properties of any substance. 17