Calorimetery

HEAT When a hot body is put in contact with a cold one, the former gets colder and the latter warmer. From this observation it is natural to conclude that a certain quantity of heat has passed from the hot body to the cold one. Heat is a form of energy. Heat is felt by its effects. Some of the effects of heat are : (a) Change in the degree of hotness (b) Expansion in length, surface area and volume (c) Change in state of a substance (d) Change in the resistance of a conductor (e) Thermo e.m.f. effect SI Unit : J (joule) Also measured in the unit calorie. (i) Calorie It is defined as the amount of heat required to raise the temperature of 1 g water by 1°C. (ii) International calorie International calorie is the amount of heat required to raise the temperature of 1g water from 14.5 °C to 15.5 °C rise of temperature. (iii) Kilo Calorie Kilo calorie is defined as the amount of heat required to raise the temperature of 1 kg water from 14.5 °C to 15.5 °C. (1 kcal = 1000 calorie). (iv) British thermal unit (B. T. U.) It is the amount of heat required to raise the temperature of one pound water by 1°F. (1 B.T.U. = 252 calorie). MECHANICAL EQUIVALENT OF HEAT According to Joule, work may be converted into heat and vice–versa. The ratio of work done to heat produced is always constant. W = constant (J) W = J H H W must be in joule, irrespective of nature of energy or work and H must be in calorie. J is called mechanical equivalent of heat. It is not a physical quantity but simply a conversion factor. It converts unit of work into that of heat and vice–versa. J = 4.18 joule/cal or 4.18 × 10³ joule per kilo–cal. For rough calculations we take J = 4.2 joule/cal SPECIFIC HEAT (s or c ) It is the amount of energy required to raise the temperature of unit mass of that substance by 1°C (or 1K) is called specific heat. It is represented by s or c. If the temperature of a substance of mass m changes from T to T + dT when it exchanges an amount of heat dQ with its surroundings then its specific heat is c = 1 dQ m dT THERMAL PROPERTIES OF MATTER The specific heat depends on the pressure, volume and temperature of the substance. For liquids and solids, specific heat measurements are most often made at a constant pressure as functions of temperature, because constant pressure is quite easy to produce experimentally. SI unit : CGS unit : cal/g –°C joule/kg–K Specific heat of water : cwater = 1 cal/g–°C = 1 cal/g–K = 1 kcal/kg–K = 4200 joule/kg–K When a substance does not undergo a change of state (i.e., liquid The temperature dependence of the specific heat of water at 1 atmospheric pressure is shown in figure. Its variation is less than 1% over the interval from 0 to 100°C. Such a small variation is typical for most solids and liquids, so their specific heats can generally be taken to be constant over fairly large temperature ranges. The temperature dependence of the specific heat of water at 1 atm Specific heat (cal/g °C ) remains liquid or solid remains solid), then the amount of heat required to raise the temperature of mass m of thesubstance by an amount  is Q = ms 1.008 1.004 1.000 0 20 40 60 Temperature (°C) 80 (i) There are many processes possible to give heat to a gas. A specific heat can be associated to each such process which depends on the nature of process. (ii) Value of specific heats can vary from zero (0) to infinity. (iii) Generally two types of specific heat are mentioned for a gas – (a) Specific heat at constant volume (Cv) (b) Specific heat at constant pressure (CP) (iv) These specific heats can be molar or gram. MOLAR HEAT CAPACITY The amount of energy needed to raise the temperature of one mole of a substance by 1°C (or 1K) is called molar heat capacity. The molar heat capacity is the product of molecular weight and specific heat i.e., Molar heat capacity C = Molecular weight (M) × Specific heat( c)  C  1  dQ    µ  dT  If the molecular mass of the substance is M and the mass of the substance is m then number of moles of the substance µ = m M  dQ  C    M m  dT  SI Unit : J/mol–K THERMAL CAPACITY The quantity of heat required to raise the temperature of the whole of that substance through 1°C is called thermal capacity. The thermal capacity of mass m of the whole of substance of specific heat s is = ms Thermal capacity = mass × specific heat Thermal capacity depends on property of material of the body and mass of the body. SI Unit : cal/°C or cal/K, Dimensions : ML2 T –2K–1 WATER EQUIVALENT OF A BODY As the specific heat of water is unity so the thermal capacity of a body (ms) represents its water equivalent also. (i) Mass of water having the same thermal capacity as the body is called the water equivalent of the body (ii) The water equivalent of a body is the amount of water that absorbs or gives out the same amount of heat as is done by the body when heated or cooled through 1°C. Water equivalent= mass of body × specific heat of the material (w = ms). LATENT HEAT OR HIDDEN HEAT When state of a body changes, change of state takes place at constant temperature [melting point or boiling point] and heat released or absorbed is Q = mL where L is latent heat. Heat is absorbed if solid converts into liquid (at melting point) or liquid converts into vapours (at boiling point) and heat is released if liquid converts into solid or vapours converts into liquid. (i) Latent heat of fusion It is the quantity of heat (in kilocalories) required to change its 1 kg mass from solid to liquid state at its melting point. Latent heat of fusion for ice : 80 kcal/kg = 80 cal /g. (ii) Latent heat of vaporization The quantity of heat required to change its 1 kg mass from liquid to vapour state at its boiling point. Latent heat of vaporisation for water : 536 kcal/kg = 536 cal/g CHANGE OF STATE (i) Melting Conversion of solid into liquid state at constant temperature is known as melting. (ii) Boiling Evaporation within the whole mass of the liquid is called boiling. Boiling takes place at a constant temperature known as boiling point. A liquid boils when the saturated vapour pressure on its surface is equal to atmospheric pressure. Boiling point reduces on decreasing pressure. (iii) Evaporation Conversion of liquid into vapours at all temperatures is called evaporation. It is a surface phenomenon. Greater the temperature, faster is the evaporation. Smaller the boiling point of liquid, more rapid is the evaporation. Smaller the humidity, more is the evaporation. Evaporation increases on decreasing pressure that is why evaporation is faster in vacuum. Heat of evaporation Heat required to change unit mass of liquid into vapour at a given temperature is called heat of evaporation at that temperature. (iv) Sublimation Direct conversion of solid in to vapour state is called sublimation. Heat of sublimation Heat required to change unit mass of solid directly into vapours at a given temperature is called heat of sublimation at that temperature. (v) • Camphor and ammonium chloride sublimates on heating in normal conditions. • A block of ice sublimates into vapours on the surface of moon because of very–very low pressure on its surface Condensation The process of conversion from gaseous or vapour state to liquid state is known as condensation . These materials again get converted to vapour or gaseous state on heating. (vi) Hoar frost Direct conversion of vapours into solid is called hoar frost. This process is just reverse of the process of sublimation. Ex. : Formation of snow by freezing of clouds. THERMAL PROPERTIES OF MATTER (vii) Regelation Regelation is the melting of ice caused by pressure and its resolidification when the pressure is removed. Ice shrinks when it melts, and if pressure is applied, deliberately promoting shrinkage, it is found that melting is thereby assisted. In other words, melting of cold ice is ordinarily effected by raising the temperature, but if pressure is present to help with the shrinkage the temperature need not be raised so much. Ice heals up after being cut through by the wire. Melting takes place under the wire because pressure lowers the melting temperature. Refreezing (regelation) occurs above the wire when the water escapes to normal pressure again. Increase of pressure lowers the melting (or freezing) point of water. Conversely, if a substance expands on melting, the melting point is raised by pressure. PHASE OF A SUBSTANCE The phase of a substance is defined as its form which is homogeneous, physically distinct and mechanically separable from the other forms of that substance. Phase diagram A phase diagram is a graph in which pressure (P) is represented along the y–axis and temperature (T) is represented along the x–axis. Characteristics of Phase diagram (i) Different phases of a substances can be shown on a phase diagram. (ii) A region on the phase diagram represents a single phase of the substance, a curve represents equilibrium between two phases and a common point represents equilibrium between three phases. (iii) A phase diagram helps to determine the condition under which the different phases are in equilibrium. (iv) A phase diagram is useful for finding a convenient way in which a desired change of phase can be produced. PHASE DIAGRAM FOR WATER The phase diagram for water consists of three curves AB, AC and AD meeting each other at the point A, these curves divide the phase diagram into three regions. Region to the left of the curve AB and above the curve AD represents the solid phase of water ( ice). The region to the right of the curve AB and above the curve AC represents the liquid phase of water. The region below the curves AC and AD represents the gaseous phase of water (i.e. water vapour). A curve on the phase diagram represents the boundary between two phases of the substance. Along any curve the two phases can coexist in equilibrium (i) Along curve AB, ice and water can remain in equilibrium.This curve is called fusion curve or ice line. This curve shows that the melting point of ice decreases with increase in pressure. (ii) Along the curve AC, water and water vapour can remain in equilibrium. The curve is called vaporisation curve or steam line. The curve shows that the boiling point of water increases with increase in pressure. (iii) Along the curve AD, ice and water vapour can remain in equilibrium. This curve is called sublimation curve or hoar frost line. TRIPLE POINT OF WATER The three curves in the phase diagram of water meet at a single point A, which is called the triple point of water. The triple point of water represents the co–existance of all the three phases of water ice water and water vapour in equilibrium. The pressure corresponding to triple point of water is 6.03 × 10 –3 atmosphere or 4.58 mm of Hg and temperature corresponding to it is 273.16K. • Significance of triple point of water Triple point of water represents a unique condition and it is used to define the absolute temperature. While making Kelvin's absolute scale, upper fixed point is 273.16 K and lower fixed point is 0 K. One kelvin of temperature is fraction 1 of the temperature of triple point of water.. 2 7 3 .16 HEATING CURVE If to a given mass (m) of a solid, heat is supplied at constant rate and a graph is plotted between temperature and time as shown in figure is called heating curve. THERMAL PROPERTIES OF MATTER (i) In the region OA Rate of heat supply P is constant and temperature of solid is changing with time So, Q = mcS T  P t = mcS T [Q Q = P t]  solid cS  T = The slope of temperature–time curve so specific heat of t 1 specific heat (or thermal capacity) is inversely proportional to the slope of temperature– slope of line OA time curve. (ii) In the region AB Temperature is constant, so it represents change of state, i.e., melting of solid with melting point T 1. At point A melting starts and at point B all solid is converted into liquid. So between A and B substance is partly solid and partly liquid. If LF is the latent heat of fusion then Q = mLF  L F  P (t 2  t1 ) [as Q = P(t2 – t1]  LF length of line AB m i.e., Latent heat of fusion is proportional to the length of line of zero slope. [In this region specific heat (iii) 1 = ] tan 0 In the region BC Temperature of liquid increases so specific heat (or thermal capacity) of liquid will be inversely proportional to the slope of line BC, c L  (iv) 1 slope of line BC In the region CD Temperature in constant, so it represents change of state, i.e., liquid is boiling with boiling point T2. At C all substance is in liquid state while at D is vapour state and between C and D partly liquid and partly gas. The length of line CD is proportional to latent heat of vaporisation, i.e., LV Length of line CD. [In this region specific heat  1 = ] tan 0 The line DE represents gaseous state of substance with its temperature increasing linearly with time. The reciprocal of slope of line will be proportional to specific heat or thermal capacity of substance in vapour state. LAW OF MIXTURES (a) When two bodies (one being solid and other liquid or both being liquid) at different temperatures are mixed, heat will be transferred from body at higher temperature to a body at lower temperature till both acquire same temperature. The body at higher temperature released heat while body at lower temperature absorbs it, so that Heat lost = Heat gained. Principle of calorimetry represents the law of conservation of heat energy. (b) Temperature of mixture (T) is always  lower temperature (TL) and higher temperature (TH), TL T TH The temperature of mixture can never be lesser than lower temperature (as a body cannot be cooled below the temperature of cooling body) and greater than higher temperature (as a body cannot be heated above the temperature of heating body). Further more usually rise in temperature of one body is not equal to the fall in temperature of the other body though heat gained by one body is equal to the heat lost by the other. Ex. 5g ice at 0°C is mixed with 5g of steam at 100°C . What is the final temperature? Sol. Heat required by ice to raise its temperature to 100°C, Q1 = m1L1 + m1c11 = 5 × 80 + 5 × 1 × 100 = 400 + 500 + 900 = 1800 cal Heat given by steam when condensed Q2 = m2L2 = 5 × 536 = 2680 cal As Q2 > Q1. This means that whole steam is not even condensed. Hence temperature of mixture will remain at 100°C. Ex. A calorimeter of heat capacity 100 J/K is at room temperature of 30°C. 100 g of water at 40°C of specific heat 4200 J/kg–K is poured into the calorimeter. What is the temperature of water in calorimeter? Sol. Let the temperature of water in calorimeter is t. Then heat lost by water = heat gained by calorimeter (0.1) × 4200 × (40 – t) = 100 (t – 30)  42 × 40 – 42t = 10t – 300  t = 38.07°C Ex. Find the quantity of heat required to convert 40 g of ice at –20°C into water at 20°C. Given Lice = 0.336 × 106 J/kg. Specific heat of ice = 2100 J/kg–K, specific heat of water = 4200 J/kg–K Sol. Heat required to raise the temperature of ice from –20°C to 0°C = 0.04 × 2100 × 20 = 1680 J Heat required to convert the ice into water at 0°C = mL = 0.04 × 0.336 × 106 = 13440 J Heat required to heat water from 0°C to 20°C = 0.04 × 4200 × 20 = 3360 J Total heat required = 1680 + 13440 + 3360 = 18480 J Ex. Steam at 100°C is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at 15°C till the temperature of the calorimeter and its contents rises to 80°C. What is the mass of steam condensed? Latent heat of steam = 536 cal/g. Sol. Heat required by (calorimeter + water) Q = (m1c1 + m2c2)  = (0.02 + 1.1 × 1) (80 – 15) = 72.8 kcal If m is mass of steam condensed, then heat given by steam Q = mL + mc  = m × 536 + m × 1 × (100 – 80) = 556 m  556 m = 72.8  Mass of steam condensed m = 72.8 556  0.130 kg