Mechanical Engineering Thermodynamics and Work Modes
Explore the concept of work in mechanical engineering thermodynamics, different work modes, such as mechanical and boundary work, and how work is calculated through force and distance integration. Dive into examples like expansion in a piston-cylinder assembly and the polytropic process to understand the relationship between pressure, volume, and work.
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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 ( ) = by the system F on the system F s dW d 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, 2 V 2 = dW pdV 1 V = dW Fdx ( pA dx ( pA 1 V = 2 ) )dV W pdV = dW 12 V 1 = dW In order to find the work done, the pressure-volume relationship needs to be known. Work is a path function! A = dW pdV 5
Boundary Work is a Path Function V = 2 W pdV 12 V 1 p p Process A Process B 1 1 W 2 2 W 12,A 12,B V V W W 12,A 12,B 6
The Polytropic Process This process is common in many thermodynamic analyses. A polytropic process obeys the following relationship, ???????? ?? = p n constant pV ? = 1 constant V V V 2 2 = = W pdV dV 12 n V V 1 1 2 W 12 V The constant can be evaluated anywhere on the process curve. Therefore, W = n n p V p V V V 2 2 = dV dV 1 V 1 n 2 V 2 n 12 V V 1 1 7
The Polytropic Process Evaluation of the integral For the case where ? ? For the case where n = 1, p V V V V 2 = = ln W dV p V 1 V 1 2 12 1 1 V 1 1 The polytropic process defines a relationship between end states, n = = n constant p V pV p V p p V V = 2 1 n n 1 2 1 1 2 2 8
The Polytropic Process Ideal Gas n p p V V The previous relationship is valid, independent of the fluid, = 2 1 1 2 If the fluid behaves like an ideal gas, n / / p p V V mRT mRT p p = = 2 1 1 1 1 2 2 2 This leads to two additional relationships for ideal gases, ( ) 1 / 1 n n n T T p p T T V V = = and 2 2 2 2 1 1 1 1 9
The Polytropic Process Ideal Gas Previously we defined the work done during a polytropic process to be: n p V p V p V n V 2 = = for 1 W dV n 1 V 1 n 2 2 1 1 12 1 V 1 However, if the fluid behaves like an ideal gas that relationship can be written as: ( 1 ) mR T T = 2 1 for 1 W n 12 n 10
Some New Terminology ... An aergonic process A process that occurs without any work modes Example: A process in a sealed, rigid container (without any shaft work) An adiabatic process A process that occurs without any heat transfer modes Example: A process that occurs in an insulated container Example: A process that happens so quickly that there isn t time for heat to be transferred 11
