Heat and the First Law of Thermodynamics - Assignment Example

Heat and the first law of thermodynamics Name Institution Date Course Heat and energy transfer Energy is defined as the capacity that a substance has that result in the substance performing some work. Energy is therefore, a property of the substance. On the other hand, heat may be defined as energy in transition. It is a form of energy and can be expressed as specific heat capacity in Kj/KgK. Expressed in this form, it represents the potential of a substance to store heat absorbed from the surroundings. The current understanding of heat and its characteristics, however, was based on early works of experimentation and research that revealed interesting results that fascinated the early scientists. The 18th and early 19th century scientists had the thought that all bodies had an invisible fluid within them which was called caloric. Several properties were assigned to this fluid, but most importantly, the fluid was believed to flow from hot bodies into cold ones. More recent experimental results have revealed that just like work, heat is a transient commodity. It is thermal energy in transit as a result of spatial temperature difference. It only exists during communication between two points of different energy levels. Consider two objects cool enough so that they radiate negligible energy. If these objects make contact with one another, the cooler object becomes hotter while the hotter object gets cooler. This happens because energy gets transferred from the hotter object to the cooler object through conduction. This transfer of energy is known as heat flow while the energy transferred referred to as heat. It is therefore, important to note the following characteristics of heat: -Heat exists in transition, that is, heat only exists when the system and its surrounding changes state. Only energy is associated with the final and initial states of the system and the surrounding, and not heat -The net effect of heat results in the change of the internal energy of any given system and the surrounding in accordance with the first law. If the change within the surroundings is a net change in a reservoir’s temperature, then heat has flowed between the surroundings and the system. The amount of heat that has flowed between the system and surrounding is directly related to the change of the reservoir’s surrounding. First law of thermodynamics and Mechanical equivalent of heat An American known by the name Benjamin Thompson was the first one to bring out the idea that heat was a form of energy and not a fluid. The American, later known as Count Rumford, when he was boring out cannons to make his arsenal as war minister of Bavaria recorded findings that led to the partial definition of heat energy as the interaction of two substances that occurs because of the difference of temperatures between the two substances. Rumford discovered that a connection existed between the heat generated and the motion of the bore. Findings have however revealed that heat energy will not always cause rise in temperature. This phenomenon can be seen when objects undergo change of state like vaporization and condensation (Moss, 1998). During the first half of the 19th century, it was found that mechanical energy as a result of friction is completely transformed to heat. This process, however, was found to be independent of the course of transformation process as well as the chemical and physical characteristics of the material used. These findings led to the definition of heat as disorganized, macroscopic and invisible movements at the molecular level. The works of Joules and his experiments on temperature differences brought a new understanding of heat and energy. Joule showed that each calorie contained 4.16 metrics of energy. Today it is known that a calorie is equivalent to 4.186 metric units of energy (Joules). These findings led to the widely accepted theory that energy is conserved in all physical processes (Hassani, 2011). Scientists have investigated energy both external and internal of objects. Findings have revealed changes in the energy levels within an environment and the surroundings during thermodynamic processes like compression and expansion of gaseous materials. Interests have been also drawn to the internal energies of a system as opposed to considerations of the system with reference to a particular frame of reference. For instance, a spinning container full of gas has kinetic energy with reference to a stationary observer. The internal energy of the gas, however, is defined with consideration to a coordinate system that is fixed on the container. The internal energy, at the microscopic level, can take several forms such as The potential energy of the particles within the system. For instance, a crystal made up of dipolar molecules experiences a change in its potential energy when an electrical field is applied to the system The kinetic energy of the molecules Energy stored internally in the form of molecular rotations and vibrations Internal energy stored as chemical bonds that may be released during a chemical process. Joule’s experiments between 1843 and 1848 made great contributions to the first law of thermodynamics. During these experiments, Joule used two-process cycles that were carried out on a system that comprised a fluid. Work was done on a paddle wheel by way of dropping a known mass through some known distance. Since the mass was tied onto the paddle using a string that was then wound around the arm of the paddle, the falling mass caused the paddle to rotate within the fluid system as shown below (Arora, 2001). The amount done by the mass was determined finding the change in potential energy of the mass as it falls through the distance z. This resulted to a rise in temperature within the fluid. In process 2-1, the fluid was placed in contact with a water bath and heat was transferred to the water until the original state of the fluid was restored. The actual amount of heat transferred (Q) to the water was determined by finding the increase in energy of the water bath. Joule repeated these experiments for different amounts of work interactions, making recordings of the corresponding amounts of heat transferred to restore the fluid to its original state. He finally reached the conclusion that the net work input W was directly proportional to the heat Q transferred for all measurements. Since at the end of any given cycle there is not effective change in state, a conclusion is reached that the algebraic sum of interactions of work during a thermodynamic cycle is zero (Arora, 2001). Joules findings led to the statement of the first law of thermodynamics as: “When a system undergoes a cycle, the cyclic integral of the heat added equals the cyclic integral of the work done.” Mathematically, this may be written as The law, as stated above, places no restrictions that limit its application to reversible energy transformation. In this form, the law applies to both reversible and irreversible transformation. There is need therefore, for a more general formulation of this law to accommodate non-cyclic process. This may be achieved by introducing the concept of internal energy. The law may therefore be stated as: “Heat and work are mutually convertible but given that creating or destroying energy is not possible, the total energy associated with an energy conversion remains constant” This means that a given amount of work must always be done so as to realize a similar temperature rise obtained with a unit amount of heat. Again, whether or not the temperature of the fluid was raised by heat transfer or work transfer, it is possible to return the fluid in opposite direction to its original state by heat transfer (Rajput, 2010). These findings led to the conclusion that work and heat are different forms of a more general thing called energy. The change in internal energy of a given substance can therefore be stated as: ∆U = Q-W From this definition, Q remains positive when heat gets into the system and W remains positive while work is done to the system. The internal energy therefore, is sum of all kinds of energy that is stored within the system. This energy is a state function and is dependent on the state of equilibrium of the system while Q and W are determined by the thermodynamic path between two equilibrium states. These findings mean that whenever a physical system goes through a complete cycle, the algebraic sum of the work transfers during any cycle §dW is directly related to the algebraic sum of the heat transfers during the cycle §dQ. This may be expressed mathematically as Where J represents the proportionality constant referred to as Mechanical Equivalent of heat. This quantity’s SI unit value is 1Nm/J (Giancoli, 2008). When a system executes a process, the effective change in the internal energy of the system is equal to the result of the heat interactions minus the total work interactions during the process. Therefore, if E is the total internal energy of the system, then: E2 – E1 = Q – W So that ∆E = Q – W [or Q = ∆E + W] 2 Or ∫1 d(Q – W) = ∆E = E2 – E1 If all other energies are absent from the system (chemical, electric and magnetic), and any changes in the kinetic and potential energy of a closed loop system are not considered, the equation above may be expressed as 2 ∫1 d(Q-W) = ∆U = U2 – U1 So that Q – W = ∆U = U2 –U1 From here, it is easy to see that the work done is given by W = Q - ∆U = Q – (U2 –U1) In general terms, addition of heat onto a system raises the temperature of the system and external work is performed as a result of the increase in the volume of the system. The increased temperature indicates an increase in the internal energy of the system. An isolated system This is a system where no interaction between the system and the surroundings is possible. This system does not have any work input, that is: dQ = 0, dW = 0 According to the first law of thermodynamics, dE = 0 and E = constant The energy of an isolated system is therefore always constant. The first law of thermodynamics and the mechanical equivalent of heat have been applied to various real life applications where energy has been converted from one form to another for a various uses. Shielding energy transfer systems from external interferences and leakages has been used to increase system efficiencies. Currently, engines have been made that have converted chemical energy of fuels to mechanical energy to great efficiency levels. Such applications were developed from the understandings of the law of nature. Energy conversion and energy transfer are used in other applications like furnaces, refrigerators, etc (Al-Shemmeri, 2010). The concepts of transfer on heat and energy from one substance to another have been greatly used in practice. One such application is the heat exchanger which is used to transfer thermal energy between different fluids, between solids and fluids or between a fluid and solid particulates, at different temperatures and in thermal contact. In these devices, normally, no external heat and work interactions are needed. Typically, the devices are used for heating or cooling a fluid stream and during evaporation or condensation of fluid streams. In some heat exchangers, fluids exchanging heat get into direct contact while in other cases the substances are separated by a heat transfer surface. Electromagnetic energy waves are the major means of heat transfer through space and it is through these waves that the heat from the sun reaches the earth through a process known as radiation. Conduction and convection are other more common means of heat transfer through solids and liquids. These are experienced during cooking, room heating and other processes where heat is transferred from one place to another. Molar specific heat of gases When something is heated, like water or soup, it is supplied with an amount of heat ∆Q which will raise the absolute temperature by an amount ∆T. the heat capacity of the substance is given by the ration of the supplied heat to the change in the temperature of the substance. That is: Heat capacity is ∆Q/∆T Speaking in the strict sense, this quantity is the average heat capacity over the concerned temperature range, since the quantity of heat needed to raise the temperature from 300K to 305K may not be the same as that required to raise the temperature of the same substance from 350K to 355K. Specific heat capacity is the heat capacity of a substance per unit mass, that is, it is the heat capacity of one kilogram of the substance. Molar specific heat is defined as the amount of heat that if supplied to a substance, will raise one mole of the substance by one degree Celsius. In order to increase the temperature of one mass of gas by 1 degree Celsius, more heat energy will be needed if the gas is kept at a constant pressure than when the gas is maintained at constant volume. This is particularly important in gaseous substances which easily vary in volume when exposed to rising temperatures. The volume of solids and liquids will also change when exposed to higher temperatures, but this change may not be significant. If heat is supplied to a gas that is allowed to expand at constant pressure then some of the heat that is supplied is absorbed in extra work and only part of it goes towards raising the temperature of the gas. More heat will therefore be required to raise the temperature of the gas. If the volume of the gas is kept constant, all the heat supplied goes towards raising the temperature so that less heat will be needed to raise the temperature of fixed volume amount of gas by 1 degree Celsius. Gases, therefore, have several specific heat capacities. The most important, however, are the specific heat capacity at constant pressure, Cp and specific heat capacity at constant volume Cv. As has been seen in the discussion above, Cp>Cv. The same applies to the molar specific heat capacity of gases. The SI unit for molar specific heat capacity is J mole-1K-1. Consequently, the expression for calculating the molar specific heat for gases is as follows: Cv = (∂U/∂T)v But since Cp is assopiated with extra energy so that we have CpdT = CvdT + PdV Since for one mole of ideal gas at fixed pressure, R dT = P dV, we have for ideal gas Cp = Cv + R Where Cp and Cv are the molar heat capacities for an ideal gas. In heating and warming applications, great energy savings are realized when this understandings are put to use. In most cases, therefore, gases are heated at high pressures. The pressure helps to bring the gas particles much closer to one another so that heat transfer between molecules occurs faster. Gases are then heated much faster and with greater efficiencies. List of References Giancoli, DC, 2008, Physics for scientists and engineers with modern physics 4th edition, Pearson, New Jersey Hassani, S, 2011, From Atoms to Galaxies: A Conceptual Physics Approach to Scientific Awareness, CRC press, Florida Moss, K, 1998, Heat and Mass in Building Services Design, Taylor & Fransis, Oxon Arora, CP, 2001, Thermodynamics, Tata McGraw-Hill Education, New York City Rajput, RK, 2010, A textbook of Engineering Thermodynamics, Firewall Media, New Delhi Al-Shemmeri, T, 2010, Engineering Thermodynamics, Tarik Al-Shemmeri & Ventus Publishing ApS, ISBN 978-87-7681-670-4 Read More