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Liquid thermometers. Based on thermal expansion of liquids. The liquids are held in little vessels at the bottom. At higher temperatures they expand and climb toward the top of narrow capillaries. How to calibrate a liquid thermometer?. You need some reference temperatures .
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Liquid thermometers Based on thermal expansion of liquids. The liquids are held in little vessels at the bottom. At higher temperatures they expand and climb toward the top of narrow capillaries.
How to calibrate a liquid thermometer? You need some reference temperatures. You may want to stick the thermometer into boiling water and melting ice, hoping that those set two well-defined temperatures. You will find the liquid expended and its column risen. What next? We can divide the column height difference into N (say, N = 100) even intervals and call them degrees. Would it be a good temperature scale? Would it be the same, no matter what liquid we use?
Liquid thermometers Coefficients of thermal expansion b – fractional increase of volume per one degree • Problems: • Liquid is a rather complex state of matter. Molecules in liquids are held together by cohesive forces, different for different liquids. • The coefficients of thermal expansion vary a lot between liquids, and may depend on temperature in an extreme fashion. • Liquids freeze at low temperatures and boil at high temperature. So the ranges of operation of the liquid thermometers are restricted.
Gas thermometer Gasses are much simpler than liquids. The molecules are moving freely most of the time, and only once in a while suffer short term collisions. The collision events are still different for different molecules…. BUT: when the gasses are rarified (low density) and the collisions are rare behavior of different gasses in the gas thermometer becomes very much the same! In order not to change the gas density, it is preferable to keep the gas volume constant and to measure the gas pressure.
Gas thermometer Level of the mercury in the right tube is varied to keep the level in the left tube constant. Pressure of the gas is measured as P =rgh The absolute temperature of the system is defined as: P3is pressure of the gas at a special reference point called “triple point”, which is unique and can be reproduced in every laboratory.
Gas thermometer To set the temperature scale we need some convenient reference points. 273.15 K, the same as 0 °C is the temperature of ice melting at normal pressure; 373.15 K, the same as 100 °C is the temperature of water boiling at normal pressure; 1K temperature difference is the same as 1 °C temperature difference, but 0 K corresponds to -273.15 °C.
Temperature scales Fahrenheit Celsius Lord Kelvin
Thermometers: summary. • Thermometers always measure their own temeparature. • For a thermometer to measure the temperature of the system of interest, it needs to be brought into thermal equilibrium with the system (and better insulated from everything else). • A thermometer must be much smaller than system. • For fast temperature measurements, it should be small and have low heat capacity. An array of miniature thermometers An array of bolometers
Heat is not a material or a from of matter. Heat is energy in transit! When pouring water you transfer it from one vessel to another and you get more water in the second vessel. In thermodynamics you transfer heat but you usually end up having more or less internal energy. Heat is positive when the system of interest obtains it.
What are common results of heat transfer? • Growth of temperature. • A phase transition (melting ice). • Mechanical work. • In cases #2 and #3 there may be NO temperature variation. Case #1, no phase transition or work done. How much does the temperature vary? Heat capacity of the object C, measured in J/K; tells you how much Joules of heat you need to transfer to increase the temperature of the object by 1 K (or 1 ºC). Heat is energy in transit! Positive, when obtained.
Heat capacity of the object C, measured in J/K; tells you how much Joules of heat you need to transfer to increase the temperature of the object by 1 K (or 1 ºC). The term “heat capacity” is used for historic reasons and is confusing! It sounds as if the object “contains heat”, whereas by definition heat is energy in transit. An object contains some internal energy (not heat!) and its temperature is a measure of this internal energy. An analogy from mechanics: you do some work on an object and the object gains the same amount of energy (kinetic, potential) as a result. Mechanical work also relates to a process, not state.
Heat capacity is an extensive (integral) parameter: When you bring two objects together, heat capacity of the system of the two objects becomes the sum of the two individual heat capacities. It is convenient to introduce specific heat, c, which is heat capacity of a material per unit mass. Specific heat is measured in J/(Kkg). Heat capacity of a water balloon is large due to both high specific heat and large mass of the water inside the ball.
Specific heat, c, is heat capacity of a material per unit mass. Specific heat is measured in J/(Kkg).
The equilibrium temperature. Situation: two objects with different temperatures, T1 and T2,are brought in a thermal contact and reach thermal equilibrium at a temperature T after a while. HeatDQ1 is transferred to Object 1; heat DQ2 is transferred to Object 2. By energy conservation: By definition of heat capacity and specific heat:
Heat transfer • Conduction. • Convection • Radiation
Setting:A rectangular slab of thickness Dx and with an area A.The front side of the slab is at a temperature T; the back side has a somewhat different temperature, T+DT.We are trying to calculate the heat-flow rate, the amount of heat flowing through the slab per unit time,H = DQ/Dt. We expect H to be proportional to the area of the slab, the temperature difference, DT, between the back and the front and inversely proportional to the thickness of the slab, Dx. H should also somehow depend of properties of the material the slab is made of…
