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HEAT & THERMODYNAMICS, , , , , , , , HEAT & THERMODYNAMICS, , , , , , , , , , Psd eld a el, , In this topic, we discuss various phenomenas involving, thermal and how does a matter behave on experiencing the, flow of thermal energy. Primarily we study, , + Thermal Expansion, + Heat & Clariometry, , ‘. Heat Transfer, , , , 1.1 Temperature and Heat, , , , , , , , Temperature : Temperature is a relative measure of hotness, or coldness of a body., , SI Unit : Kelvin (k), , Commonly Used Unit : °C or °F, Conversion : t,=t,,+273.15, , , , Heat : Heat is a form of energy flow (i) between two bodies, or (ii) between a body and its surroundings by virtue of, temperature difference between them, , SI Unit : Joule (J), Commonly Used Unit : Calorie (Cal), Conversion : leal= 4.186 J, , + Heat always flows from a higher temperature system, to a lower temperature & system., , , , 1.2. Measurement of Temperature, , , , , , , , Principle : Observation of Thermometric property with the, change in temperature and comparing it with certain, reference situations., , . Reference situation is generally ice point or steam point., , 1.2.1 Celcius and Fahrenheit Temperature Scales, , In Celsius Scale, , , , In Fahrenheit Scale, , , , Ice point > 0°C Ice point > 32°F, , Steam point > 1000°C Steam point + 212°F, , , , , , , , , , It implies that 100 division in celcius scales is equivalent to, 180 scale divisions in fahrenheit scale., , t,-32_, Hence > =, , 180 100, , , , , , , , S}, , Temperature (°F), , , , O, g Temperature (°C) 100 &, , Absolute Temperature Scale, , It is kelvin scale, , , , , , , , Ice point > 273.15 K, Steam point > 373.15 K, Comparing it with the celcius scale, number of scale division, , in both the scales is same., , t,-0°C _ t,—273.15, , , , 100 100, . Kelvin scale is called as absolute scale, because it is, practically impossible to go beyond OK in the negative, side., seam 7 373.15 K 100°C 212.0°C, ‘oint, Ice a °C, point fF] 273-15K orc orc, Absolute 1) ox -27315°C -27315°C, zero, Kelvin Scale Celcius Scale Fahrenheit Seale, (]" [| ec (| 18°F, Comparison of Temperature Scales, , , , , , , , 3 Thermometers, , Instrument used to measure temperature of any system is, called as thermometer., , Examples : Liquid in Glass thermometer, Platinum Resistance, Thermometer, Constant Volume Gas Thermometers.
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Liquid in Glass thermometer and Platinum Resistance, thermometer give uniform readings for ice point & steam point, but go non uniform for different liquids and different materials., , Constant volume gas thermometer gives same readings, respective of which gas. It is based on the fact that at low, pressures and constant volume, P x T for a gas., , , , Pressure, , , , -273.15°C oc ‘Temperature, , ec), , , , , , , , All gases converge to absolute zero at zero pressure., , 1.3. Thermal Expansion, , It is widely observed, that most materials expand on heating, and contract on colling., This expansion is in all dimensions., , Experimentaly it has been observed that fractional change, in any dimension is proportional to the change in, temperature., , , , , , constant (k), , , , , , , , , , , , , , , , , , , , Linear Expansion =a AT Coefficient of Linear expansion (a) :, C0 Increase in length per unit length per degree rise in temp., AL, : AA . ., Area Expension A =B AT Coefficient of Area Expansion (B) :, BAL : . «, Increase in area per unit area per degree rise in temp., . AV eae oF ., , Volume Expansion wot AT Coefficient of volume expansion (y) :, , , , , , , , , , , , , , , , , , Increase in area per unit volume per degree rise in temp., , , , , , Units of a, B, y=/°C or /K, , In general with change in volume the density will also, change., , «a for metals generally higher than a for non-metals, , 7 is nearly constant at high temperatures but all low temp, it depends on temp., , , , r(10°K")
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HEAT & THERMODYNAMICS, , , , Coefficient of volume expansion of Cu as a function of, temperature., , For ideal gases y is inversely propertional to temp. at, constant pressure, , nRT AV _ AT, v= > =, P Vv T, ppaatil, " T, , As an exception, water contracts on heating from 0°C to, 4°C andhence its density increases ftom 0°C to 4°C. Thus, is called as anamolous expansion, , , , , , , , (a), , , , , , In general, y=3a=58, , Proof : Imagine a cube of length, / that expands equally in, , all directions, when its temperature increases by small AT;, , We have, , Al= alAT, , Also, , AV = (Al —, , =3PAl, , P+3P Al+ 31AP +AP—P, , , , A), Tn Equation (1) we ignore BIAP & AP as Al is very small as, compared to /., , So, 3V Vo», AV= 1 Al = 3VaAT (Using 1 =P} (2), WY esa, Vv, y=3a., , Similarly we can prove for area expansion coefficient, In case, thermal expansion is prevented inside the rod by, fixing its ends rigidly, then the rod acquires a compre:, strain due to external fones at the ends corresponding stress, set up in the rod is called thermal stress., , ssive, , , , , , Also, , we know, , AV 3 :, 7 = aAT =compressive strain, , yol, YO" =o = Thermal stress, , 3), , Practical applications in railway tracks metal tyres of cart, wheels, bridges and so many other applications., , o, =yaAT, , , , 14, , , , , , Heat & Calorimetry, , , , , , or, , When two systems at different temperatures are connected, together then heat flows from higher temperature to lower, temperature till the time their temperatures do not become, same., , Principle of calorimetry states that, neglecting heat loss to, surroundings, heat lost by a body at higher temperature is, equal heat gained by a body at lower temperature., , heat gained = heat lost, , Whenever heat is given to any body, either its temperature, changes or its state changes., , 1.4.1 Change in Temperature, , When the temp changes on heating,, , Then, , Heat supplied o change in temp (AT), a amount of substance (m/n), @ nature of substance (s/C), , AH = msAT, , m= Mass of body, , s = specific heat capacity per kg, , AT = Change in temp, , AH = nCAT, , n=Number of moles, , C= Specific/Molar heat Capacity per mole, , AT = Change in temp, , Specific Heat Capacity : Amount of heat required to raise, the temperature of unit mass of the substance through one, degree., , Units, , SI> J/KgK S,.o = L cal/g°C, , Common Cal/gC? Syoie) = 0.5 cal/g°C
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HEAT & THERMODYNAMICS, , , , Molar Heat Capacity : Amount of heat required to raise the, temperature of unit mole of the substance through one degree, , Units, SI J/molK, Common > Cal/ge?, , Heat Capacity : Amount of heat required to raise the, temperature of a system through one degree, , => AH=SAT, where S = Heat Capacity, Units, SI>J/K, Common -> Cal/C°, , For H,0 specific heat capacity docs change but fairly very, les:, , , , Materials with higher specific heat capacity require a lot of, , heat for some a given in temperature, , , , , , 1.4.2 Change in state, , , , , , When the phase changes on heating, Then, , Heat supplied @ amount of substance which changes the, state (M), , a nature of substance (L), => AH=mL, Where L = Latent Heat of process, , Latent Heat : Amount of heat required per mass to change, the state of any substance., , Units, SI> I/Kg, Common — Cal/g, , The change in state always occurs at a constant, temperature., , For example, Sodid = Liq L,, , Liq = Gas L,, L,= Latent Heat of fusion, , L, = Latent heat of vaporization, , In case any material is not at its B.P or M.P, then on heating, the temperature will change till the time a particular state, change temperature reaches., , For Example : If water is initially at50°C at 1 Atm pressure, in its solid state., , , , On heating., , Step -1: Temp changes to 0°C first, , Step -2: Ice melts to H,O(/) keeping the temp constant, Step -3: Temp. inverses to 100°C, , Step -4: H,O(/) boils to steam keeping the temp constant, , Step -5: Further temp increases, , , , , , , , , , Temp, Heat, * The slope is inversely proportional to heat capacity., . Length of horizontal line depends upon mL for the process., , , , 1.4.3 Pressure dependence on melting point and boiling point, , , , . For some substance melting point decreases with increases, pressure and for other melting point increases, , . Melting poing increases with increase in temperature. We, can observe the above results through phaser diagrams., , , , , , , , , , , , A, TEC) TCC), For HO For CO,, LineAO — Sublimation curve, LineOB —> Fusion curve, LineOC — Vapourization curve, PointO -— Triple Point, , PointC — Critical temperature, , Triple Point: The combination pressure and temperature, at which all three states of matter (i.e. solids, liquids gases, co-exist., , For H,O itis at 273.16K and 0.006 Atm., , Critical Point : The combination of pressure & temp, beyond which a vapour cannot be liquified is called as, critical point., , Corresponding temperature, pressure are called as critical, temperature & critical pressure.
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‘HEAT & THERMODYNAMICS, , , , From the phasor diagram, we can see that melting point, decreases with increases in pressure for H,O., , Based on this is the concept of reglation., , Reglation : The phenomena of refreezing of water melted, below the normal melting point due to addition of pressure., , It is due to this pressure effect on melting point that cooking, is tough on mountains and lasier in pressure cooker., , , , 15, , , , Heat Transfer, , , , , , There are three modes of heat transfer., Conduction, , Convection, , Radiation, , , , 1.5.1 Conduction, , , , , , , , Thermal conduction is the process in which thermal energy, is transferred from the hotter part of a body to the colder, one or from hot body to a cold body in contact with it, without any transference of material particles., , , , T.>Tp, , Direction of, heat flow, , , , , , , , , , At steady state,, , The rate of heat energy flowing through the rod becomes, constant., , (T=), L, , This is rate Q=kA (i), , , , for uniform cross-section rods, where Q = Rate of heat energy flow (J/s or W), A= Area of cross-section (m’), , T..T,, = Temperature of hot end and cold end respectively, (°C orK), , L=Length of the rod (m), , K = coefficient of thermal conductivity, , Coefficient of Thermal Conductivity : It is defined as, amount of heat conducted during steady state in unit time, through unit area of any cross-section of the substance, under unit temperature gradient, the heat flow being normal, to the area., , Units, , SI > J/mSk or W/mK., , Larger the thermal conductivity, the greater will be rate of, heat energy flow for a given temperature difference., , K,, , mete > Koon metas, Thermal conductivity of insulators is very low. Therefore,, air does not let the heat energy to be conducted very easily., , For combinations of rods between two ends kept at different, temperatures, we can use the concept of equivalent thermal, conductivity of the composite rod., , For example :, , , , , , , , , , T[_LKA_|, , , , T)_L,2L,A_|T,, , , , , , , , , , , , , , , , , , , , , , where K,, for equivalent thermal conductivity of the, compositive., , (T. -T, ), L, , The term in the above equation is called as, , Temperature Gradient., , Temperature Gradient : The fall in temperature per unit, length in the direction of flow of heat energy is called as, Temperature Gradient, , Units, SI> Kim, , The term Q, (i.e.) rate of flow of heat energy can also be, named as heat current, , The term (L/KA) is called as thermal resistance of any, conducting rod., , Thermal Resistance : Obstruction offered to the flow of, heat current by the medium, , Units > K/W, , , , Convection, , The process in which heat is transferred from one point to, another by the actual movement of the heated material, particles from a place at higher temperature to another place, of lower temperature is called as thermal convection., , If the medium is forced to move with the help of a fan or a, pump, it is called as forced convection., , If the material moves because of the differences in density, of the medium, the process is called natural or free, convection., , Examples of forced convection, , Circulatory system, cooling system of an automobile heat, connector
