ENG2002 Thermodynamics I Unit 7 PDF

University of Technology, Jamaica Faculty of Engineering and Computing ENG2002 – Thermodynamics I Unit 7: The 1st Law and Thermal Energy in Closed Systems Prepared by: Dr Paul A Campbell School of Engineering ...

University of Technology, Jamaica Faculty of Engineering and Computing ENG2002 – Thermodynamics I Unit 7: The 1st Law and Thermal Energy in Closed Systems Prepared by: Dr Paul A Campbell School of Engineering  OBJECTIVES Define the concept of thermal energy and its relationship to temperature. Differentiate between specific heat at constant volume and specific heat at constant pressure. Define enthalpy and its relationship to internal energy. Calculate change in internal energy and enthalpy for various substances including ideal gases, solids and liquids Utilize information on specific heats to perform 1st Law analyses for various substances. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 2  Approach to Solving Process Problems 1. Sketch the system and show energy interactions across the boundaries. 2. Create a property table, making slots for most important properties. 3. Identify the “initial” state (Units 2 to 4), and enter known properties in table. 4. Determine other “initial” properties using tables or EOS (Units 2 to 4) and enter values into table. 5. Do energy analysis. (Units 5 to 7). Where appropriate: Apply the 1st law to determine work, heat and other “final” properties, and/or Determine work: use appropriate equation based on the type of substance and process, and/or For EOS substances undergoing single-phase process, heat capacity relation. 6. Determine other “final” properties using tables or EOS ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 3  Internal Energy in Single Phase Processes Remember the nature of internal energy: Potential Energy Atom-to-Atom Chemical Energy Molecule-to-Molecule Phase/Latent Energy For EOS processes Neutron/Proton-to-Neutron/Proton Nuclear Energy Kinetic Energy Translation of Molecules Rotation of Molecules Thermal Energy – Energy manifested in temperature changes Vibration of Molecules (Spring between atoms) ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 4  E.g. Thermal Energy in a Gas Consider these two systems: Molecules have the same speed in both systems. The same number of molecules is in both systems. System B has less volume than System A. We can deduce: Both have the same thermal A energy (micro-KE). Therefore both systems have the same temperature. B System B has a higher pressure than System A. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 5  Internal Energy in Single Phase Processes Conclusion: Internal Energy (Thermal) is only a related to temperature, and not pressure or volume. Not absolutely true, but a reasonable approximation. The property that relates how temperature and internal energy are related is called heat capacity. Approximately, A At very high pressures B (or very small volumes) molecules become close enough that latent energy changes begin to play a role. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 6  Measuring Specific Heat Capacity Heat substance in a rigid container for Heat substance in a piston-cylinder cv. device for cp. 3.12 kJ ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 5.19 kJ 7  Specific Heat Capacity SPECIFIC HEAT CAPACITY AT CONSTANT VOLUME, cv The energy required to raise the temperature of the unit mass of a substance by one degree holding volume constant… or … The change in the internal energy of a substance per unit change in temperature at constant volume. SPECIFIC HEAT CAPACITY AT CONSTANT PRESSURE, cp The energy required to raise the temperature of the unit mass of a substance by one degree holding pressure constant… or … The change in the enthalpy of a substance per unit change in temperature at constant pressure. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 8  Specific Heat Capacity For single-phase processes, we are primarily concerned with determining Δu, rather than just u. Remember from Math, Now, if we say z = u, x = T and y = v, then Remember that we define , Therefore, we can say For single-phase processes, we know that this term can be neglected… Therefore, for single-phase processes, we can approximate ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 9  Finding Δu: Using cv When your substance is tabulated, just read u1 and u2 from the u tables. Directly from Tables When substance is defined by an EOS, then use cv cv,2 2 If an equation for cv(T) is known, then cv,ave do the integration. Numerical cv,1 True Δu Integration If cv(T) is tabulated, then approximate. 1 Approximate Δu Approximation NEVER USE for processes when there is a change of phase. T1 T2 T ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 10  Ideal Gas: Energy Analysis For ideal gases, cp and cv are related by cp and cv are also related by the specific heat ratio, k or γ. When the ideal gas is air, if told to assume constant heat capacities, use these values for cp and cv. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 11  Incompressible Substances Like ideal gases, incompressible substances are an idealization. Liquids and solids can be assumed to behave like incompressible substances. For truly incompressible substances cp = cv = c. Even for incompressible substance, c can vary with temperature. Therefore, When the substance is water, if told to assume constant heat capacities, take c = 4.182 kJ/kg·K. (Remember Joule’s Experiment?) ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 12  E.g. 1: Energy Analysis – Ideal Gases If the electrical heater is on for 5 minutes, using both tables and average specific heats methods, determine the T and V of state 2. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 13  E.g. 2: Energy Analysis – Ideal Gases If Wsh = 0.02 hp for 30 minutes, using both tables and average specific heats methods, determine the P, T, and V of state 2. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 14  E.g. 3: Energy Analysis – Real Steam A piston–cylinder device contains steam initially at 1 MPa, 450°C, and 2.5 m3. Steam is allowed to cool at constant pressure until it first starts condensing. a) Show the process on a T-v diagram with respect to saturation lines b) determine the mass of the steam, c) determine the final temperature, d) determine the amount of heat transfer, and e) determine the work done by the steam. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 15  E.g.: Energy Analysis – Ideal Gases 4. A piston–cylinder device, whose piston is resting on a set of stops, initially contains 3 kg of air at 200 kPa and 27°C. The mass of the piston is such that a pressure of 400 kPa is required to move it. Heat is now transferred to the air until its volume doubles. Assume cv = 0.85 kJ/kg.K a) Show the process on a P-v diagram. b) Determine the work done by the air and c) Determine the total heat transferred to the air during this process. 5. Air is expanded isothermally at 100C from 0.4 MPa to 0.1 MPa. Find the ratio of the final to the initial volume, the heat transfer, and work. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 16  E.g. 6: Energy Analysis Incompressible Substance During a picnic on a hot summer day, all the cold malta drinks disappeared quickly, and the only available drinks were those at the ambient temperature of 29 °C. Another 24-case of 330 ml malta drinks, is placed in an igloo-chest with ice. Determine the mass of ice that will melt by the time the canned drinks cool to 8°C. Assume the malta drink to have the same thermal properties as water. ENG2002 - Unit 7: Thermal Energy and 1st Law Analysis of Closed Systems, Paul Campbell 17