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Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Lecture 10 Work as an Energy Transport Mode What is Work? From Physics 211 … dW Fby the system Fon the system d s Questions … Is work a vector or a scalar? When you integrate dW do you get W2 – W1? What is the significance of dW ? In ME 322 …work can occur in several different ways. However, they are all analogous to a ‘force’ through a ‘distance’. 2 Possible Work Modes Mechanical Work Other types of Work 3 Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Moving Boundary Work P(dV) Work Moving Boundary Work Example: Expansion of a fluid in a piston-cylinder assembly The work done can be found by integration, dW Fd x dW pA d x dV dW pA A dW pdV 5 2 dW 1 W12 V2 pdV V1 V2 pdV V1 In order to find the work done, the pressure-volume relationship needs to be known. Work is a path function! Boundary Work is a Path Function W12 p V2 pdV V1 p Process A 1 1 W12,A 2 W12,B V W12,A W12,B 6 Process B 2 V The Polytropic Process This process is common in many thermodynamic analyses. A polytropic process obeys the following relationship, p pV n constant 1 W12 W12 2 V2 V1 pdV V2 V1 constant dV n V V The constant can be evaluated anywhere on the process curve. Therefore, V2 V2 p1V1 n p2 V2 n W12 dV dV n n V V V1 V1 7 The Polytropic Process Evaluation of the integral results in, W12 V2 V1 p1V1 n p2 V2 p1V1 dV n V 1 n for n 1 For the case where n = 1, W12 The polytropic process defines a relationship between end states, 8 V2 V1 p1V1 V2 dV p1V1 ln V V1 pV constant n p1 V1 n p2 V2 n p2 V1 p1 V2 n The Polytropic Process – Ideal Gas The previous relationship is valid, independent of the fluid, p2 V1 p1 V2 n If the fluid is an ideal gas, n p2 V1 mRT1 / p1 p1 V2 mRT2 / p2 This leads to two additional relationships for ideal gases, T2 p2 T1 p1 9 n 1 / n 1 n and T2 V2 T1 V1 The Polytropic Process – Ideal Gas The work done during a polytropic process is, W12 V2 V1 p1V1 n p2 V2 p1V1 dV n V 1 n for n 1 If the fluid is an ideal gas, W12 10 mR T2 T1 1 n for n 1 Some New Terminology ... • An aergonic process – A process that occurs without any work modes – Example: A process in a closed, rigid container • An adiabatic process – A process that occurs without any heat transfer modes – Example: An process that occurs in an insulated container 11