PA F ext A dV dl If non flow piston moves slowly the external force and the

Pa f ext a dv dl if non flow piston moves slowly the

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PA F ext A dV dl / If non-flow piston moves slowly the external force and the differential distance moved by piston in cylinder are: Substitute and cancel out the cross- sectional area “A”. Express either as extensive or intensive quantities: (kJ) PdV dW (kJ/kg) Pdv dw Work is positive into system and negative out of system. The negative sign maintains the sign convention
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© Heriot-Watt University 15 Heat Capacity The heat capacity is the amount of energy a substance can store per unit mass (or mole) per unit temperature rise: V V T u C Heat Capacity of Constant Volume: Increase in internal energy for small change in temperature keep volume constant Heat Capacity of Constant Pressure: P P T h C Increase in enthalpy for small change in temperature keep pressure constant The heat capacity may be specific (kJ/kg K) or may be molar (kJ/kmol K) thus “u” or “h” may be specific (kJ/kg) or molar (kJ/kmol). The units must be consistent.
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© Heriot-Watt University 16 Internal Energy and Enthalpy Internal energy: “u” is the total kinetic and potential energy of all the molecules in a system. It depends on the T & P of a substance. It can be both specific “u” (kJ/kg) or molar “u” (kJ/kmol). It is an energy storage term a thermodynamic property. Enthalpy: “h” is an auxiliary property of internal energy - it includes the additional “pressure energy” term “Pv”. It too depends on the T & P of a substance. It too can be specific “h” (kJ/kg) or molar “h” (kJ/kmol). It too is an energy storage term a thermodynamic property. It is linked to internal energy through definition: Pv u h
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© Heriot-Watt University 17 1.2 Non-Flow Processes 1. Constant Volume Process: If volume is constant then boundary is rigid and fixed, no work can be done if boundary cannot move. ) (J Q Only heat may enter or leave the system: Heat in is positive. Heat out is negative 1 2 u u q The non-flow energy equation then simply reduces to either intensive or extensive forms: 1 2 u u m Q Or,
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© Heriot-Watt University 18 dT du C V dT C du V dT C u u T T V 2 1 1 2 dT C q T T V 2 1 Constant Volume Heat Balance For an ideal- gas internal energy “u” is a function of temperature only (independent of pressure) - thus Integrating left and right leads to Substitute result back into non-flow expression yields dT C m Q T T V 2 1 Or,
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© Heriot-Watt University 19 Non-Flow Processes 2. Constant Pressure Process: In this case the boundary moves, so both heat and work may be transferred. For a constant pressure process the non-flow expressions are: Heat and work transferred to system is positive. Heat and work transferred from system is negative ) (J Q ) (J W 1 2 v v P w 1 2 h h q
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© Heriot-Watt University 20 dT dh C P dT C dh P dT C h h T T P 2 1 1 2 dT C q T T P 2 1 Constant Pressure Heat Balance For an ideal- gas internal energy “h” is also a function of temperature only (independent of pressure) - thus Integrating left and right leads to Substitute result back into non-flow expression gives dT C m Q T T P 2 1 Or,
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© Heriot-Watt University 21 Constant Volume Heat Balance Summary
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