2Today’s main concepts: Introduce Specific Heats, cv and cP.Understand when it is acceptable to apply specific heat.Calculate changes of energy using specific heatsFor liquids and solids, the saturated properties values may be used to approximate properties values for supercooled property values, if the model can be treated as incompressible.For incompressible liquids and solids, cv ≈ cpthe specific heat ratio is defined as k = cp/cvReading Assignment:Read Chap 3: Sections 11Homework Assignment:From Chap 3: 49, 55,68, 78
3Think back to those simple, happy, carefree days of your youth, back when you were in Physics lab…. You performed experiments to try and figure out how the world around you worked.In one experiment you dropped hot aluminum pellets into a container of water and measured the change of temperature the water underwent.… it requires 1 calorieof heat to raise thetemperature of1 gram of waterby 1 deg C.Using that information you found a property of aluminum calledspecific heat capacity.
4-- Used to calculate changes of energy between states Sec 3.9 : Specific HeatIn Thermodynamics, two common forms of specific heat capacity are used.andConstant VolumeprocessConstant Pressureprocess-- Used to calculate changes of energy between states-- Defined for pure, simple compressible substances-- May be used only under certain “special conditions”-- Usually applied to “ideal gas” modelWhen it can be applied: (if cv and cp are often treated as constants)and
5This is an exact differential Sec 3.9 : Specific HeatSpecific HeatsTvisobarsT1T2the internal energy change or enthalpy change when heat is added at constant pressure or constant volume.At constant volumeThis is an exact differentialwhereAt constant volume, dV=0; thus,Finally:
6This is an exact differential Sec 3.9 : Specific HeatisobarsTvT1T2At Constant PressureThis is an exact differentialwhereAt constant pressure, dP=0; thus,Finally,
7For air (at 68oF (20oC) and 14.7 psia (1 atm)): Sec 3.9 : Specific HeatSpecific Heat Ratio:For air (at 68oF (20oC) and 14.7 psia (1 atm)):
8Fig03_09 Fig. 3.9 Shows that cv and cp for water/steam vary with temperature and pressure.Fig03_09
9In practice, specific heats will be used as constants which are looked up on tables based on standard values of temperature and pressure.Fig03_09Example of Table:Gases - Specific Heats and Individual Gas Constants
10Evaluating Properties of Liquids and Solids: While Appendix A does have a table for super-cooled water, for many other liquids, a super-cooled table is not available.What to do?For liquids and solids, it is acceptable practice to approximateandif a super cooled table is not available.
11Evaluate liquids at the saturated state Sec : Approximations for Liquids using Saturated DataFor a liquid, there is little change in v, u, h, s at different pressure and fixed T. Therefore,Evaluate liquids at the saturated stateSince these properties are essentially only a function of T and not P, we call them Incompressible.
12Example:What is the enthalpy for Refrigerant 22 at T = 10 deg F. and p = 40 psi. (Refer to Table A-7E)pressurespec. vol.*T=10 deg Cp = 40 psiTemperaturespec. vol.*oat T=10 deg….hf=13.33 Btu/lbm
13For liquids and solids: Sec : Incompressible Substance ModelIncompressible Substance: Includes any substance whose properties do not change with pressure.For liquids and solids:ThusBut,So now what? Take partial with respect to TThus,
14Use the heat capacity to calculate the change in internal energy. Sec : Incompressible Substance ModelUse the heat capacity to calculate the change in internal energy.If c = constant then that means,is small and can usually be droppedTherefore,
15Table of specific heat for incompressible materials. See the course website for the complete tables of specific heats for both compressible and incompressible materials.