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Unit 61: Engineering Thermodynamics Lesson 5: Work Objective NDGTA • The purpose of this lesson is to consider the concepts of work and heat. Work NDGTA • Work is often defined as the product of force and the distance moved in the direction of the force. This is the mechanical definition of work. • A more general definition of work is the thermodynamic one: Work, an interaction between a system and its surroundings, is done by a system if the sole external effect on the surroundings could be the raising of a weight. Work NDGTA Piston Cylinder Velocity W Gas Work being done by expanding gas in a cylinder Work NDGTA • The convention chosen for positive work is that if the system performs work on the surroundings it is positive. • A piston compressing a fluid is doing negative work, whereas a fluid expanding against a piston is doing positive work. • The units of work are force x distance i.e. N.m or J or lb-ft Power NDGTA • The rate of doing work, designated W is called power. • The units of power are J.s-1 or Watts or ft.lbf.s1. • Sometimes power is measure in horsepower defined as 1 hp = 0.746kW = 550 ft-lbf.s-1. Power NDGTA Resistor battery Note: if no energy were to cross the system boundary, then no work would be done. It is therefore important to determine the system boundary in thermodynamics Quasi-equilibrium Work due to a Moving Boundary NDGTA • There are a number of modes of work that occur in engineering for example… – – – – the work needed to stretch a wire, or to rotate a shaft, or to move against friction, or To cause a current to flow through a resistor or to charge a capacitor • In thermodynamics we are primarily concerned with the work required to move a boundary against a pressure force. Quasi-equilibrium Work due to a Moving Boundary NDGTA • Consider the piston-cylinder arrangement from previous. Consider that there is a seal to contain the gas in the cylinder, that the pressure is uniform throughout and that there are no gravity effects, magnetic or electric effects. • This assures us of a quasiequilibrium process, one in which the gas is assumed to pass through a series of equilibrium states. Quasi-equilibrium Work due to a Moving Boundary NDGTA • Now allow an expansion of the gas to occur that sees the piston move a small distance, ds. • The force acting on the piston is the pressure times the area of the piston. • This pressure is expressed as absolute pressure since pressure is a result of molecular activity – any molecular activity will yield a pressure which will result in work being done when the boundary moves. Quasi-equilibrium Work due to a Moving Boundary NDGTA • The infinitesimal work which the system (the gas) does on the surroundings (the piston) is then the force multiplied by the distance… δW = PAdS but Ads is dV (differential volume) • Thus as the piston moves from some position s1 to another position s2, the above expression can be integrated to give… V W1-2 = PdV 2 V1 Quasiequilibrium Work due to a Moving Boundary NDGTA • This assumes that the pressure is known for each position as the piston moves from volume V1 to V2. The work W1-2 is the crosshatched area under the P-V curve P P 1 1 PdV PdV 2 V1 V2 2 V V1 V2 V Quasi-equilibrium Work due to a Moving Boundary NDGTA • Note 1: the area representing the work is very dependent upon the path – i.e. the states 1 and 2 are the same in both diagrams yet the areas are different. Thus work is a function of path. The differential of a path function is called an inexact differential. • Note 2: the pressure P is assumed to be constant throughout the volume at each intermediate position. Quasi-equilibrium Work due to a Moving Boundary NDGTA • Example: 1-kg of steam with a quality of 20% is heated at a constant pressure of 200kPa until the temperature reaches 400oC. Calculate the work done by the steam. V2 PdV = P(V2 – V1) = mP(v1 – v2) W1-2 = V1