Experiments of Heat Capacity - Assignment Example

Heat Capa Experiments in Physics indicate that the change in a body’s internal energy is directly proportional to the subsequent change in temperature, that is, ∆U α ∆T. As such, the physical quantity known as heat capacity, C, would be given by: C = limit(∆T 0)( ∆U/∆T). Therefore, heat capacity, also referred to as thermal capacity, is defined as the amount or quantity of heat or thermal energy needed to raise a body’s temperature by a single unit of temperature (Hewitt, Suchocki, & Hewitt, 2012). Thus: C = Q/∆T where Q is the heat energy and ∆T is the temperature change. From this definition, the derived SI unit for heat capacity is Joule per Kelvin, JK-1. According to Hewitt et al. (2012), two factors determine the heat capacity of a body; the material it is made of and its mass. For instance, it would take 2 minutes to heat an electric kettle holding about 1.6 kg of water from 200C to 600C while it will take 100 minutes to heat a hot water tank holding about 160 kg of water by the same temperature with a 5 kW immersion heater. Energy = Power * Time 1 kW = 1,000 W Hence, 5kW = 5 * 1000 = 5,000W For the kettle, energy = 5,000W * (2 * 60sec) = 600,000J For the hot water tank, energy = 5,000W * (100 * 60sec) = 30,000,000J ∆T = 600C – 200C = 400C or 40K Thus, the heat capacity for the water in the kettle will be: 600,000J/40K = 15,000JK-1 What will be the heat capacity for the water in the hot water tank? (750,000JK-1) This explains why it takes longer waiting for hot water tanks to heat up water for bathing than would be the time waited for kettles to boil. The water contained in hot water tanks have higher heat capacities that the water in kettles. Hence, it would require more energy to raise the temperature of the water in the hot water tank than it would be required to raise the temperature in the kettle. Taking the same mass of different materials, it would take different times to raise their temperatures by equal magnitude using the same electric heater. Thus, Avison (2009) documents various heat capacities for 1 kg of different materials as shown in Figure 1. Figure 1: Times taken to raise the temperature of 1 kg of different materials by 100C. From “The World of Physics,” by J. Avison, 2009. Measuring the heat capacity of a substance with reference to its specific mass gives its specific heat capacity. Hewitt et al. (2012) define specific heat capacity, c, as the heat energy required to raise the temperature of a kilogram of a substance by 1 Kelvin. Hence: c = Q/m∆T = C/m where m is the mass of the substance in kilograms The SI unit for specific heat capacity is J(kgK)-1. Taking the example above, the specific heat capacity would be: For heating up the water in the kettle, c = 600,000J/1.6kg * 40K = 9,375 J(kgK)-1 What would be c for heating up the water in the hot water tank? (6,400 J(kgK)-1). Note that experimental values tend to be higher than the exact specific heat capacities of various substances because of the heat losses during heating (Avison, 2009). Due to such difficulties in determining the specific heat capacities of substances, they have been documented for referencing. Table 1 shows some specific heat capacities for various substances. Table 1. Specific heat capacities for selected substances From “The World of Physics,” by J. Avison, 2009 Example: A hot water tank has 160kg of water at 200C. Calculate: (a) The heat energy required to raise the water temperature to 600C and (b) The time taken given an electric immersion heater of 5kW. (a) Temperature rise, ∆T = 600C – 200C = 400C = 40K c = 4,200J(kgK)-1 Q = cmVT = 4,200J(kgK)-1 * 160kg * 40K = 26,880,000J (b) Power = Energy * Time Time = Energy/Power = 26,880,000J/5,000W = 5,376s. Relevance to Physical Science The knowledge of heat capacity, and specific heat capacity by extension, informs on the heating characteristics of substances. As such, it plays a critical role in determining the substances to use when making instruments where the heating characteristics of such substances are of basic importance. Therefore, substances that have a small specific heat capacity heat up quickly and additionally experience a huge change in temperature despite supplying a small amount of heat. Those with high specific heat capacities tend to take long to heat up and also lose heat slowly, thus good insulators and coolants (Avison, 2009). The knowledge of heat capacity has also been used to explain the expansion of various gases. Practical Use in Physical Science Physical science has practically benefitted from the knowledge on heat capacity. As such, substances that have a small specific heat capacity would be used in making equipment that require fast conduction of heat such as cooking instruments like pots, kettle and frying pans among others. This is because they quickly heat up even on exposure to small amount of heat (Hewitt et al., 2012). The same principle has been used to make sensitive thermometers using materials with small specific heat capacities that would rapidly and accurately detect and show slight changes in temperature. On the other hand, substances with high specific heat capacities find wide application in making insulators such as kettle handlers. This is because exposure to heat would only result in small changes in temperature of such substances and would therefore not heat up fast. Furthermore, heat storage instruments would be made from such instruments with high specific heat capacities as they tend to retain heat as opposed to conducting heat away. This knowledge has seen water being used as a cooling agent for engines as it takes long to warm due to its high specific heat capacity, thus cools the engine for long before it heats up (Hewitt et al., 2012). It is also widely used in cold areas to heat up houses because on boiling water, it retains heat and warm the house as a result of its high specific heat capacity. References Avison, J. (2009). The world of physics. Cheltenham: Thomas Nelson and Sons. Hewitt, P. G., Suchocki, J. A., & Hewitt, L. A. (2012). Conceptual physical science (5th ed.). Upper Saddle River: Pearson Education. Read More