DAIRY CHEMISTRY AND BIOCHEMISTRY mately 700kPa at 20C), all of which are interrelated. Since the osmotic pressure of milk remains essentially constant(because it is regulated by that of the cow's blood), the freezing point is also relatively constant The freezing point of an aqueous solution is governed by the concentra- tion of solutes in the solution. The relationship between the freezing point of a simple aqueous solution and concentration of solute is described by a relation based on Raoult s law: T=Ke (11.10) where T is the difference between the freezing point of the solution and that of the solvent, K is the molal depression constant( 1.86C for water) and m is the molal concentration of solute. However, this equation is valid only for dilute solutions containing undissociated solutes. Raoult's law is thus limited to approximating the freezing point of milk The freezing point of bovine milk is usually in the range -0.512 to 0.550C, with a mean value close to -0.522C( Sherbon, 1988)or 0.540C (Jenness and Patton, 1959). Despite variations in the conc tions of individual solutes, the freezing point depression of milk is quite constant since it is proportional to the osmotic pressure of milk(approxi mately 700kPa at 20 C), which is regulated by that of the cows blood. The freezing point of milk is more closely related to the osmotic pressure of mammary venous blood than to that of blood from the jugular vein. Owing to their large particle or molecular mass, fat globules, casein nicelles and whey proteins do not have a significant effect on the freezing point of milk, to which lactose makes the greatest contribution. The freezing nt depression in milk due to lactose alone has been calculated to be 0.296.C. Assuming a mean freezing point depression of 0.522 C, all other constituents in milk depress the freezing point by only 0. 226C. Chloride is also an important contributor to the colligative properties of milk. Assum ing a CI concentration of 0.032 M and that Cl- is accompanied by a monovalent cation (i.e. Na or K), the freezing point depression caused by CI" and its associated cation is 0. 119C. Therefore, lactose, chloride and its accompanying cations together account for about 80% of the freezing point depression in milk. Since the total osmotic pressure of milk is regulated by that of the cows blood there is a strong inverse correlation between lactose and chloride concentrations( Chapter 5) Natural variation in the osmotic pressure of milk(and hence freezing point)is limited by the physiology of the mammary gland. variations in the freezing point of milk have been attributed to seasonality, feed, stage of lactation, water intake, breed of cow, heat stress and time of day. These factors are often interrelated but have relatively little infuence on the freezing point of milk. Likewise, unit operations in dairy processing which do not influence the net number of osmotically active molecules/ ions in solution do not influence the freezing point, Cooling or heating milk causes444 DAIRY CHEMISTRY AND BIOCHEMISTRY mately 700 kPa at 20"C), all of which are interrelated. Since the osmotic pressure of milk remains essentially constant (because it is regulated by that of the cow's blood), the freezing point is also relatively constant. The freezing point of an aqueous solution is governed by the concentra￾tion of solutes in the solution. The relationship between the freezing point of a simple aqueous solution and concentration of solute is described by a relation based on Raoult's law: Tf = K,m (11.10) where is the difference between the freezing point of the solution and that of the solvent, K, is the molal depression constant (136°C for water) and m is the molal concentration of solute. However, this equation is valid only for dilute solutions containing undissociated solutes. Raoult's law is thus limited to approximating the freezing point of milk. The freezing point of bovine milk is usually in the range -0.512 to -O.55O0C, with a mean value close to -02~22°C (Sherbon, 1988) or - 0.540"C (Jenness and Patton, 1959). Despite variations in the concentra￾tions of individual solutes, the freezing point depression of milk is quite constant since it is proportional to the osmotic pressure of milk (approxi￾mately 700 kPa at 20"C), which is regulated by that of the cow's blood. The freezing point of milk is more closely related to the osmotic pressure of mammary venous blood than to that of blood from the jugular vein. Owing to their large particle or molecular mass, fat globules, casein micelles and whey proteins do not have a significant effect on the freezing point of milk, to which lactose makes the greatest contribution. The freezing point depression in milk due to lactose alone has been calculated to be 0.296"C. Assuming a mean freezing point depression of 0.522"C, all other constituents in milk depress the freezing point by only 0.226"C. Chloride is also an important contributor to the colligative properties of milk. Assum￾ing a C1- concentration of 0.032M and that C1- is accompanied by a monovalent cation (i.e. Na' or K'), the freezing point depression caused by C1- and its associated cation is 0.119"C. Therefore, lactose, chloride and its accompanying cations together account for about 80% of the freezing point depression in milk. Since the total osmotic pressure of milk is regulated by that of the cow's blood, there is a strong inverse correlation between lactose and chloride concentrations (Chapter 5). Natural variation in the osmotic pressure of milk (and hence freezing point) is limited by the physiology of the mammary gland. Variations in the freezing point of milk have been attributed to seasonality, feed, stage of lactation, water intake, breed of cow, heat stress and time of day. These factors are often interrelated but have relatively little influence on the freezing point of milk. Likewise, unit operations in dairy processing which do not influence the net number of osmotically active molecules/ions in solution do not influence the freezing point. Cooling or heating milk causes