THERMAL PHYSICS/EXPANSION Mr Rishi Gopie
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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
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
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 18 3. 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
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 + 273 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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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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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
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
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
The graph V vs T shows that V T ( and therefore that V/T = a constant) thus supporting Charles` law. 13
3) the Pressure law to investigate the relationship between P and T at constant V 14
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
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 - 273 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
of an absolute temperature scale since it does not depend on the properties of any substance. 17