Temperature and Thermometers PDF

VERITAS UNIVERSITY ABUJA PHY 101 (General Physics) Lecture note on Heat and Temperature Nnamdi Opara TEMPERATURE AND HEAT ENERGY Te...

VERITAS UNIVERSITY ABUJA PHY 101 (General Physics) Lecture note on Heat and Temperature Nnamdi Opara TEMPERATURE AND HEAT ENERGY Temperature is a fundamental quantity in studying heat (thermal energy) and thermodynamics. The concept of temperature however differs from heat. Temperature measures the average kinetic energy of the particles in a substance. It can also be defined as a sensation or degree of hotness and coldness of a body. A body's temperature determines the direction of the flow of heat from one body to another (from hot to cold). Heat on the other hand describes the transfer of thermal energy between molecules within a system. It is a form of energy that can be transferred from one point to another due to temperature differences. Heat measurement is usually referred to as Calorimetry while Temperature measurement is referred to as Thermometry. DIFFERENCES BETWEEN HEAT AND TEMPERATURE BASIS OF HEAT TEMPERATURE COMPARISON Definition Heat is the amount of energy in a Temperature is the measure of the body. It is a form of energy called intensity of heat (hotness or thermal energy coldness) What it measures Total kinetic and potential energy Average kinetic energy of molecules contained by molecules in an object. in a substance Units of Measurement Joule, Calorie Celsius, Kelvin, Fahrenheit Property Flows from hot to cold Rises when heated; falls when Cooled Ability to do work Yes No Measuring Device Calorimeter Thermometer Symbol Q T THERMAL EQUILIBRIUM Consider two bodies with different temperatures, one hot and the other cold, which are placed in thermal contact. The hot body has higher temperatures due to its higher heat energy. Heat energy flows from the hot body to the cold body until the temperatures are equal. At this point, the two bodies are said to be in thermal equilibrium with each other. So, a thermal equilibrium exists between two bodies when they are in thermal contact with each other and there is no net flow of heat between them. Hence, thermal equilibrium is the state in which two bodies in physical contact with each other have the same temperature. THE ZEROTH LAW OF THERMODYNAMICS The Zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other. In other words, the zeroth law means the three bodies are all at the same temperature. Therefore, in terms of thermal equilibrium, the temperature of a system is defined as that property that determines whether two or more systems are in thermal equilibrium with each other or not. PROPERTIES OF A THERMOMETRIC SUBSTANCE A thermometric substance is a material that has some physical property which changes continuously as the temperature changes. So, to measure temperature, it is necessary to select a physical property or parameter of a chosen substance which varies uniformly with temperature. A parameter or property is a variable which is assigned a constant value during a discussion or event. Some of the examples of these properties or parameters are: (i) the volume of a liquid; (ii) the volume of a gas at constant pressure; (iii) the pressure of a gas at constant volume; (iv) the electrical resistance of a conductor; (v) the EMF change of a thermocouple when there is a temperature difference between the junctions of a thermoelectric thermometer. REFERENCE TEMPERATURES Reference temperatures are temperatures at fixed points. Fixed Points are temperatures at which particular physical properties manifest themselves e.g. melting, boiling. The two types of fixed points are ice point and steam point. Ice Point (The Lower Fixed Point) This is the temperature of the melting point of pure ice or freezing point of pure water at standard atmospheric pressure. It can also be defined as the temperature at which pure ice (solid) water is in equilibrium with liquid water at standard atmospheric pressure. Ice Point is therefore the temperature at which solid and liquid water can coexist in a state of thermal equilibrium at standard pressure. This temperature is marked 0oC or 32oF. Steam Point (The Upper Fixed Point) This is also known as the boiling point of pure water. It is the temperature under standard pressure at which water evaporates as steam, or steam condenses to water. Steam point is therefore defined as the temperature when pure liquid water exists in equilibrium with water vapour at standard atmospheric pressure. This temperature is 100oC or 212oF NOTE: The difference between the upper fixed point and the Lower fixed point is called the Fundamental Interval. THE TEMPERATURE SCALES The types of temperature scales are: i. The Celsius scales. ii. The Fahrenheit scale. iii. The Absolute scale of temperature (Kelvin) I. THE CELSIUS SCALE The ice point is 0oC and the steam point is at 100oC. Each part represents 1oC. Let X represent the property of the thermometric substance, which serves as a temperature indicator. Let X0 = Ice or lower fixed point Let X100 = Steam point or upper fixed-point Fundamental interval = X100 – X0. If 𝑋𝑡 is the value of the property at an unknown temperature 𝑡𝑐, then 𝑿𝒕 − 𝑿𝟎 𝒕𝒄 = ( )× 𝟏𝟎𝟎˚𝑪 (1) 𝑿𝟏𝟎𝟎 − 𝑿𝟎 Example 1 The lengths of the mercury column of a mercury thermometer are 1.02 cm and 12.76 cm respectively at the standard fixed points. What is the temperature of a body, which produces 5.0 cm of this mercury column? Solution 5 𝑐𝑚 − 1.02 𝑐𝑚 𝑡𝑐 = × 100 °𝐶 12.76 𝑐𝑚 − 1.02 𝑐𝑚 𝒕𝒄 = 𝟑𝟑. 𝟗 °𝑪 II. THE FAHRENHEIT SCALE The ice point is 32oF while the steam point is 212oF. The fundamental interval is 180 divisions. Each division represents 10oF. Hence, 𝑿𝒕 − 𝑿𝟑𝟐 𝒕𝑭 − 𝟑𝟐 = ( )× 𝟏𝟖𝟎 (2) 𝑿𝟐𝟏𝟐 − 𝑿𝟑𝟐 𝑿𝒕 − 𝑿𝟑𝟐 ∴ 𝒕𝑭 = [( )× 𝟏𝟖𝟎] + 𝟑𝟐 (3) 𝑿𝟐𝟏𝟐 − 𝑿𝟑𝟐 On the Fahrenheit scale, 𝑋212 = 𝑋100 𝑎𝑛𝑑 𝑋32 = 𝑋0, Therefore 𝑋𝑡 − 𝑋0 𝑡𝐹 = [( )× 180] + 32 (4) 𝑋100 − 𝑋0 Substituting eq 1 into eq4 𝑡𝑐 𝑡𝐹 = [( ) × 180] + 32 (5) 100  Factorizing eqn 5 gives rise to the temperature conversion equations TEMPERATURE CONVERSIONS (a) To convert 0C to 0F 9 𝑡𝐹 = [ 𝑡𝐶 + 32] ℉ (6) 5 (b) To convert 0F to 0C 5 𝑡𝐶 = [𝑡𝐹 − 32] ℃ (7) 9 Note: 𝑡𝐹 represents temperature in Fahrenheit while 𝑡𝐶 is the temperature in Celsius Example 2 Convert 50oC to Fahrenheit scale. Solution 𝑡𝐶 = 20oC, 𝑡𝐹 =? 𝑡𝐹 = [( 9/5) 𝑡𝐶 + 32] ℉ = [ (9/5) × (50) + 32] ℉ = 122 ℉ III. KELVIN / ABSOLUTE SCALE OF TEMPERATURE / THERMODYNAMIC SCALE The ice point of the Kelvin scale is 273.15 K while its steam point is 373.15 K Absolute Zero: This is the basis of the Kelvin scale. Absolute Zero is the temperature at which everything freezes as molecules of any substance have the lowest energy at this point. This occurs at 0 K. The triple point of water is the reference point on the thermodynamic scale where saturated water vapour, pure water and melting ice are in equilibrium with each other. The temperature of the triple point of water is 273.16K. Hence the three phases of water coexist at this temperature. Kelvin to Celsius Conversion Formula TC = TK – 273.15 Celsius to Kelvin Conversion Formula TK = TC + 273.15 EXERCISES Q 1: Convert temperatures 30° Celsius to Fahrenheit. (ans: 86° F) Q.2. Convert temperature 300 Kelvin to Celsius (ans: 26.85 °C) Q.3. Convert temperature 68° Fahrenheit to Celsius (ans: 20 °C) Q.4. Convert temperature 313 Kelvin to Fahrenheit (ans: 103.73 ° F) Q.5. Convert 198° Fahrenheit to Kelvin (ans: 365.37K) TYPES OF THERMOMETERS Thermometers may be classified according to the thermometric properties used in constructing such thermometers. For example, we have: i. Liquid-in-Glass Thermometer: uses the expansion of the liquid in the glass tube. As the liquid volume increases with temperature rise, the length of the liquid along the tube varies with temperature. ii. Constant Volume-Gas Thermometer: makes use of a given mass of gas whose pressure varies with temperature at constant volume. iii. Constant Pressure-Gas Thermometer: makes use of a given mass of gas whose volume varies with temperature at constant pressure. iv. Resistance Thermometer: uses the variation of resistance of a given conductor such as platinum with temperature. v. Thermo-electric Thermometer: makes use of the variation of electromotive force (emf) developed between the pair of junctions of two dissimilar metals with temperature. vi. Optical Pyrometer: makes use of radiant energy from a hot glowing body