Lecture 4 Specific Heat - Thermal and Fluids Engineering I...

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Lecture 4 – Specific Heat Specific Heat of Ideal Gases Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree For gases, we distinguish between constant pressure processes and constant volume processes: Constant pressure: Constant volume: More heat is needed to raise a unit mass by one degree in a constant pressure process than in a constant volume process. In a constant pressure process, the added heat is converted to both internal energy and work to raise the weight. In a constant volume process, all added heat is converted to internal energy. Lecture 4 Page 1
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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski First consider the constant volume heating of a gas in a rigid tank. From the first law UQW ∆=− Since no work is done UQ ∆= If the gas is ideal, internal energy is only a function of temperature (an empirical fact). We define the specific heat at constant volume c v so that v Um cT ∆= ∆ constant specific heat, ideal gas This equation applies to all processes of ideal gases, not just constant volume ones. In differential form v dU mc dT = In general, c v is a function of temperature. () v dU mc T dT = and ( ) v Ud c T d = ∫∫ T The specific internal energy u , is defined as U u m = Specific internal energy is a thermodynamic property, like specific volume, temperature or pressure. There is an EES function for specific internal energy which is u = INTENERGY(H2, T=T1) Lecture 4 Page 2
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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Now consider heat addition in a constant pressure process. The first law is UQW ∆=− If the process is quasi-equilibrium, WP d = V 2 Because pressure is constant 21 () d VP VV PV == = UQPV ∆=−∆ QUP VUUP VV =∆ + ∆ = + Since 1 P PP we may arbitrarily rewrite this equation in the form ( 22 2 11 1 V UP V =+ −+ ) We define a new property, enthalpy, as H UP V =+ so that, 2 QH H =− 1 constant pressure, closed system Lecture 4 Page 3
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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski As it happens, the enthalpy of an ideal gas is only a function of temperature . We prove this by substituting the ideal gas law into the definition of enthalpy to get mRT HU M =+
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Lecture 4 Specific Heat - Thermal and Fluids Engineering I...

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