Newtons law of cooling, basics of thermodynamics
- 1. BUILDING SERVICESSubmitted by MUHAMMED JESWIN P K
- 3. Newtons Law of Cooling states that THE RATE OF CHANGE OF THE TEMPERATURE OF AN OBJECT IS PROPORTIONAL TO THE DIFFERENCE BETWEEN ITS OWN TEMPERATURE AND THE AMBIENT TEMPERATURE I.E. THE TEMPERATURE OF ITS SURROUNDINGS. What it means is that the rate at which an object loose or gain heat depends on the difference between its own temperature and the surrounding’s temperature The law is always tied with the condition that o The temperature difference is small between object and surroundings o The nature of heat transfer mechanism remains the same conduction, convection etc. temperature time
- 4. Rate of temperature change Temperature changing coefficient Initial temperature of object Temperature of surroundings (ambient temperature) Temperature at time t Temperature of object at time t
- 5. HEAT TRANSFER VERSION OF THE LAW The heat-transfer version of Newton's law, which requires a constant heat transfer coefficient, states that THE RATE OF HEAT LOSS OF A BODY IS PROPORTIONAL TO THE DIFFERENCE IN TEMPERATURES BETWEEN THE BODY AND ITS SURROUNDINGS. Thermal energy Heat transfer coefficient Heat transfer surface area Temperature of the object's surface and interior Temperature of the environment
- 6. APPLICATIONS o To predict how long it takes for a hot object to cool down at a certain temperature. o To find the temperature of a soda placed in a refrigerator by a certain amount of time. o It helps to indicate the time of death given the probable body temperature at the time of death and current body temperature. The heat transfer coefficient h depends upon physical properties of the fluid and the physical situation in which convection occurs. Therefore, a single usable heat transfer coefficient (one that does not vary significantly across the temperature-difference ranges covered during cooling and heating) must be derived or found experimentally for every system that can be analysed using the presumption that Newton's law will hold. LIMITATIONS OF NEWTONS LAW OF COOLING o The difference in temperature between the body and surroundings must be small, o The loss of heat from the body should be by radiation only, o The temperature of surroundings must remain constant during the cooling of the body. Newton's Law is more closely followed for forced air or pumped fluid cooling, where the velocity of the fluid does not vary with temperature. In the case of heat transfer by thermal radiation, Newton's law of cooling holds only for very small temperature changes, and a more accurate description is given by Planck's Law.
- 8. In plane walls heat transfer through the walls can be decreased by adding insulation on the surface of the wall. But in the case of cylindrical or spherical objects this may not be the case This is due to the fact that Heat transfer from an object depends on the surface area of the object By adding insulation to a plane wall, surface area is not changed, hence heat transfer is effectively dampened by insulation provided. But in the case of spherical or cylindrical or any other curved surface, adding insulation excessively could increase the surface area of the exterior enough so that insulation cannot provide heat protection similar to plane walls Adding insulation in this case decreases the convection resistance at the outer surface. The thickness upto which heat flow increases and after which heat flow decreases is termed as critical thickness. In the case of cylinders and spheres it is called CRITICAL RADIUS. The critical radius of insulation for optimum heat transfer rc= k ho Conductivity of material Heat transfer coefficient
- 9. APPLICATIONS o While deciding the thickness of insulation for an electric wire, from which you want to release the heat generated because of the passage of current, the thickness of insulation should be lower than the critical thickness value. o Finding best insulation thickness for HVAC shafts, vents, pipes carrying heated or cooled water o While designing insulation thickness for a thermos flask from which you don't want heat leakage, the thickness should be more than the critical thickness. ASSUMPTIONS FOR CALCULATING CRITICAL RADIUS o All air gaps are neglected. o Heat is assumed to be uniformly distributed o Convection between material and the covering is neglected. o Radiations losses are neglected. o Clamps used for holding the insulated rod do not absorb any heat during the process and hence aren't considered in calculations.
- 10. Example Assume a steel pipe of r1 = 10 mm, which is exposed to natural convection at h = 50 W/m2.K. This pipe is insulated by material of thermal conductivity k = 0.5 W/m.K. Determine the critical thickness of this combination: Hence rcr > r1 and heat transfer will increase with the addition of insulation up to a thickness of rcr – r1 = (0.010 – 0.005)m = 0.005 m Critical Thickness of Insulation – Spherical Coordinates It can be shown in a similar manner that the critical radius of insulation for a spherical shell is:
- 11. KIRCHHOFF’S LAW OF THERMAL RADIATION
- 12. Kirchhoff’s Law of thermal radiation: FOR AN ARBITRARY BODY EMITTING AND ABSORBING THERMAL RADIATION IN THERMODYNAMIC EQUILIBRIUM, THE EMISSIVITY IS EQUAL TO THE ABSORPTIVITY. emissivity ε = absorptivity α all bodies above absolute zero temperature radiate some heat. Two objects radiate heat toward each other. But what if a colder object with high emissivity radiates toward a hotter object with very low emissivity? This is resolved by the fact that each body must be in direct line of sight of the other to receive radiation from it. Therefore, whenever the cool body is radiating heat to the hot body, the hot body must also be radiating heat to the cool body. Moreover, the hot body will radiate more energy than cold body. The case of different emissivities is solved by the Kirchhoff’s Law of thermal radiation, which states that object with low emissivity have also low absorptivity. As a result, heat cannot spontaneously flow from cold system to hot system
- 13. The emissivity, ε, of the surface of a material is its effectiveness in emitting energy as thermal radiation and varies between 0.0 and 1.0. By definition, a blackbody in thermal equilibrium has an emissivity of ε = 1.0. Real objects do not radiate as much heat as a perfect black body. They radiate less heat than a black body and therefore are called gray bodies. Quantitatively, emissivity is the ratio of the thermal radiation from a surface to the radiation from an ideal black surface at the same temperature as given by the Stefan–Boltzmann law. Emissivity is simply a factor by which we multiply the black body heat transfer to take into account that the black body is the ideal case. The surface of a blackbody emits thermal radiation at the rate of approximately 448 watts per square metre at room temperature (25 °C, 298.15 K). Real objects with emissivities less than 1.0 (e.g. copper wire) emit radiation at correspondingly lower rates (e.g. 448 x 0.03 = 13.4 W/m2). Emissivity plays important role in heat transfer problems. For example, solar heat collectors incorporate selective surfaces that have very low emissivities. These collectors waste very little of the solar energy through emission of thermal radiation. EMISSIVITY
- 14. Another important radiation property of a surface is its absorptivity, α, which is the fraction of the radiation energy incident on a surface that is absorbed by the surface. Like emissivity, value of absorptivity is in the range 0 < α < 1.From its definition, a blackbody, which is an idealized physical body, absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. That is, a blackbody is a perfect absorber. Since for real objects the absorptivity is less than 1, a real object can not absorb all incident light. The incomplete absorption can be due to some of the incident light being transmitted through the body or to some of it being reflected at the surface of the body. In general, the absorptivity and the emissivity are interconnected by the Kirchhoff’s Law of thermal radiation visible radiation occupies a very narrow band of the spectrum from 0.4 to 0.76 nm. hence, we cannot make any judgments about the blackness of a surface on the basis of visual observations. For example, consider white paper that reflects visible light and thus appear white. On the other hand it is essentially black for infrared radiation (absorptivity α = 0.94) since they strongly absorb long- wavelength radiation. ABSORPTIVITY
- 15. APPLICATIONS Sand is rough black, so it is a good absorber and hence in deserts, days (when radiation from the sun is incident on sand) will be very hot. Now in accordance with Kirchhoff's law, good absorber is a good emitter so nights (when sand emits radiation) will be cold. This is why days are hot and nights are cold in desert. When a shining metal ball having some black spots on its surface is heated to a high temperature and is seen in dark, the black spots shine brightly and the shining ball becomes dull or invisible. The reason is that the black spots on heating absorb radiation and so emit these in dark while the polished shining part reflects radiations and absorb nothing and so does not emit radiations and becomes invisible in the dark. When a green glass is heated in furnace and taken out, it is found to glow with red light. This is because red and green are complimentary colours. At ordinary temperatures, a green glass appears green, because it transmits green colour and absorb red colour strongly. According to Kirchhoff's law, this green glass, on heating must emit the red colour, which is absorbed strongly. Similarly when a red glass is heated to a high temperature it will glow with green light. A person with black skin experiences more heat and more cold as compared to a person of white skin because when the outside temperature is greater, the person with black skin absorbs more heat and when the outside temperature is less the person with black skin radiates more energy.
- 16. Kirchoff’s law also explains the Fraunhofer lines : o Sun's innermost part (photosphere) emits radiation of all wavelength at high temperature. o When these radiation enters in outer part (chromosphere) of sun, few wavelength are absorbed by some terrestrial elements (present in vapor form at lower temperature) o These absorbed wavelengths, which are missing appear as dark lines in the spectrum of the sun called Fraunhofer lines. o During total solar eclipse these lines appear bright because the gases and vapour present in the chromosphere start emitting those radiation which they had absorbed
- 17. THANK YOU