# Chapter 3 Temperature and Heat

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1 Chapter 3 Temperature and Heat In Chapter, temperature was described as an intensive property of a system. In common parlance, we understand temperature as a property which is related to the degree of hotness (or coldness) of a substance for physical touch. It is to be noted however, that human perception regarding the degree of hotness or coldness of an object could be deceptive- because what our body senses is only the loss or gain of heat from the surroundings. For example, on a cold winter night, the atmosphere may appear to be colder when you are moving on a vehicle than when you are stationary. This is because of increased heat loss from the body to the air while in motion (due to convective effects). Similarly, on a cold morning, a metallic object appears to be colder than a wooden object, although both are at the same temperature. This can also be attributed to larger heat loss from the body to the metal due to its higher thermal conductivity. Such subjective assessments can be avoided if we employ calibrated devices for measuring temperature. The measurement of temperature hinges on the idea of equilibrium between systems. System A is said to be in equilibrium with another system B, if no changes are observed in the properties of both the systems, when they are in contact with each other. For example, if both systems are gases and pressure of A is the same as pressure of B, then the two systems are said to be in mechanical equilibrium (i.e. forces are in balance). If the two pressures are not equal, then a work interaction process will occur between the two systems until the pressures become equal. Similarly, if the temperature of A and temperature of B are equal, then the two systems are said to be in thermal equilibrium. If the temperatures of the two systems are not equal, then a heat interaction process will occur, until thermal equilibrium occurs between the systems. As a consequence of heat flow, changes in some properties can be observed for these systems and the observed property changes can be calibrated to indicate the temperature changes. The Zeroth Law of Thermodynamics, as stated below, further illustrates the idea of equilibrium: If system A is in equilibrium with system B and system B is in equilibrium with system C, then systems A and C must be in equilibrium with each other. A B C Department of Mechanical Eng Indian Institute of Technology Madras

2 Here, system B could be a thermometer, for instance. If B shows a temperature reading of 00 units while in equilibrium with A, and it shows the same temperature reading of 00 units while in equilibrium with system C, then systems A and C must both be at the same temperature. Attaining thermal equilibrium is essential for obtaining the correct reading. How many times have we felt irritated when the doctor leaves the thermometer in the mouth for a couple of minutes, in order to read the body temperature correctly when we have fever? If the thermometer is taken off soon, it would not have reached thermal equilibrium with the body and the temperature value read will be incorrect. Now let us turn our attention to the methods for measuring temperature. Any property of a substance that varies with temperature could be used for measuring temperature, after proper calibration of the associated device. For example, in a mercury thermometer, the length of a mercury column varies with temperature due to thermal expansion. Expressing the column length as a suitable function of temperature, the device can be calibrated by measuring the length at some known values of temperature. For instance, the variation of column length ( ) could be written as a linear function of temperature in the form: a b. T, if the temperature variation is not too large. For the purpose of calibration, we could use the known temperatures such as the ice point 0 o C and the steam point 00 o C. Here, ice point refers to the melting point of ice at atm pressure and steam point refers to the boiling point of pure water at atm pressure. The constants a and b can be calculated as: 00 a 0 and b 00 0 in terms of the mercury column lengths corresponding to the steam and ice point temperatures. A similar calibration procedure could be adopted for any other type of thermometer also. Liquids other than mercury may be used in a liquid-in-glass thermometer. Also, high temperature materials such as quartz may be employed instead of ordinary glass. Such modifications can change the operational temperature range of the thermometer. Temperature can also be measured by employing principles other than the linear thermal expansion of a substance. For example, the ideal gas behavior which relates the gas pressure, temperature and volume can be used to measure temperature. A thermometer constructed on this principle will be called as an ideal gas thermometer. Such a thermometer could be used in two modes, namely: the constant volume mode in which volume is constant and the pressure varies linearly with temperature; alternatively, it can be used in the constant pressure mode for which the volume varies linearly with temperature. For the constant volume mode, expressing Department of Mechanical Eng Indian Institute of Technology Madras

3 the gas pressure as p = a + b.t, the constants a and b can be obtained as discussed earlier. Indeed, for a gas of mass m, such a calibration will result in the expression R pv m. ( T 73.5) M for the relationship between the gas pressure, volume and temperature. Here, T is expressed in degree Celsius. It is also possible to define a new temperature scale known as the Kelvin scale, where temperature in Kelvin is given as temperature in degree Celsius Note that for T = o C, p 0. In other words, the calibration of the ideal gas thermometer should give: p steam pt p 00 p ice pt ice pt b a 73.5 From a microscopic point of view, temperature can be related to the average kinetic energy of the randomly moving molecules of a gas. For instance, in monatomic gases such as helium, argon, neon, etc. the average kinetic energy in each of the three directions (x,y,z) is given by: mu mv mw T Where is the Boltzmann s constant and u, v and w are the average molecular velocity components for the three directions under equilibrium conditions. Here, T is the temperature expressed in Kelvin. It is clear that as T approaches zero Kelvin, all molecular motion will cease and the pressure also will approach zero value. The pressure can be related to the molecular momentum, from the microscopic point of view. below: The other commonly employed techniques for measuring temperature are described (i) Thermo-electric effect: Let A and B represent two junctions made of two different metals M and M as shown in the figure. If the temperatures of A and B are different, then an emf (voltage) will develop. By M M M M measuring this emf, temperature can be measured. In practice, one of the junctions (cold junction) will be kept at a known temperature such as ice point and the hot junction temperature could be evaluated from the measured value of voltage. The voltage could be expressed as a function of the hot junction temperature (T) such as emf = a + b.t + c.t, where the constants A B Department of Mechanical Eng 3 Indian Institute of Technology Madras

4 a, b and c could be evaluated from calibration. These types of hot and cold junctions are known as Thermocouples. (ii) Dependence of resistance on temperature: In devices known as resistance thermometers, the electrical resistance of a wire may vary with temperature, typically in a polynomial form. For instance, if R(T) = a + b.t + c.t + d.t 3, by measuring the resistance of the wire at four known temperatures, it is possible to determine the constants a, b, c and d. Obviously, such a procedure involves the calibration of the resistance thermometer. There are also some semiconductor based devices known as thermistors for which the electrical resistance does not vary as a polynomialbut it varies exponentially with respect to temperature. The associated constants can be determined through calibration for thermistors also. (iii) Liquid crystals: For liquid crystals, the color of the crystal depends on its temperature. By relating color and temperature, it is possible to use the liquid crystal as a thermometer. (iv) Pyrometers: The temperature of a body which is at an elevated temperature can be measured with the help of the radiation emitted by the body. Devices which measure temperature from the radiation emitted by a body are known as pyrometers. For calibrating different types of thermometers, a list of known temperatures is necessary. Apart from the ice point and steam point, several other temperature values are required. These are typically phase change temperatures such as the boiling points of liquids, freezing points of metals, etc and they are called as Fixed Points. A few fixed points which are commonly employed are: Oxygen point (boiling point of liquid oxygen = o C), Sulfur point (boiling point of liquid sulfur = o C), Antimony point (freezing point of antimony = o C), Silver point (freezing point of liquid silver = 96.9 o C) and Gold point (freezing point of liquid gold = o C). Depending on the number of constants to be determined, an equal number of fixed point temperatures can be selected and employed for calibrating the temperature measuring device. Any calibrated device will indicate accurate temperature values at the fixed temperatures used for the calibration. However, at other temperatures, the measured values may have some intrinsic error. For example, consider two different devices- say, a mercury thermometer which is calibrated using the ice point, steam point and a linear interpolation function; a thermocouple which is calibrated using the temperatures of ice point, steam point, sulfur point and a quadratic interpolation function. Although both devices will read ice point as 0 o C and steam point as 00 o C, it is possible that the mercury thermometer may read a temperature value as 50 o C while the thermocouple may report the same temperature as 50.5 o C. Such small differences will exist between the data measured by different thermometers, at all temperatures except the fixed points used for calibration. Department of Mechanical Eng 4 Indian Institute of Technology Madras

5 In Chapter, heat was described as an energy interaction between the system (or CV) and the surroundings. A more precise definition for heat is that it is an energy interaction which occurs because of the temperature difference between the system (or CV) and the surroundings. Heat transfer between two objects may occur by heat conduction, convection or radiation. Conduction heat transfer occurs because of molecular collisions between two objects which are in physical contact with each other. Consider two systems A and B, with the temperature of A being greater than the temperature of B (i.e. T A > T B ). If the two systems are in physical contact, at the interface, molecules of A will randomly collide with those of B. Since T A > T B, the average molecular velocity of system A will be larger than the average molecular velocity of B. In the process, some random kinetic energy of molecules of A will be transferred to those of B due to collisions. Such energy transfer is known as heat transfer. Convection heat transfer occurs when there is relative motion between a fluid and an object. As the relative velocity increases, the rate of convective heat transfer also increases. Radiative heat exchange occurs through space. Even when two objects at different temperatures are not in physical contact, photons emitted by one can be received by the other through space. When an object is at a high temperature, some of its molecules can attain a higher energy state as a consequence of the energy exchange due to molecular collisions. When these higher energy state molecules return their ground states, they emit photons corresponding to the energy difference. Such photon exchange between hot and cold objects gives rise to radiative heat transfer. The rate of heat transfer by the three modes can be summarized as follows: Q conduction dt ka ; Qconvection ha( TA TB ) and Qradiation A( T dx The radiative heat transfer expression corresponds to the heat exchange between an object at temperature T A and the surrounding at temperature T B. In the above relations, k is the thermal conductivity of the medium, A is the surface area, h is the heat transfer coefficient, is the Stefan- Boltzmann constant and is the emissivity of the surface. 4 A T 4 B ) Some of the popular misconceptions about heat are listed below: (i) Whenever an object receives heat, its temperature will increase Wrong. During a phase change process such as boiling, melting etc. even though there may be heat addition, the temperature will not increase. (ii) If the temperature of an object increases during a process, there must have been a heat input to that object Wrong. Temperature of an object can be increased by work input also. In smithy shop, as mechanical working is carried out on an object, its temperature increases. In the context of these clarifications, revisit the above definition given for heat interaction. Department of Mechanical Eng 5 Indian Institute of Technology Madras

6 T A Q T B In the figure shown above, when system temperature T A is greater than the surrounding temperature T B, heat is transferred from the system to the surroundings. The sign convention adopted is as follows: heat added to a system is positive and heat removed from a system is negative. In other words, when heat transfer occurs from the surroundings to the system, Q > 0. If the heat transfer is from the system to the surroundings, then Q < 0. Both heat and work are energy interactions occurring across the system (or CV) boundary. Depending on how the system boundary is drawn, the classification of the interaction as heat or work could change. For example, consider a vessel filled with water which is heated by an electrical coil wound on its outside. If the system boundary is drawn such that it includes the electrical coil, then the electrical energy flowing through the coil will be treated as work. On the other hand, if the system boundary excludes the coil (and includes only the vessel with water), then the energy interaction occurring between the vessel and the coil is heat. In fact, this energy interaction takes place because the coil gets red hot due to current flow and heat is transferred from the coil to the vessel by virtue of the temperature difference. Department of Mechanical Eng 6 Indian Institute of Technology Madras

7 Department of Mechanical Eng 7 Indian Institute of Technology Madras

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