LESSON No. 9 WORK TRANSFER: In thermodynamics the work can be defined as follows:

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1 LESSON No. 9 WORK TRANSFER: In thermodynamics the work can be defined as follows: Work shall be done by the system if the total effect outside the system is equivalent to the raising of weight and this work shall be positive work. In above definition the work has been defined as positive work and says that there need not be actual raising of weight but the effect of the system behaviour must be reducible to the raising of a weight and nothing else. Its units are N. m or Joule. Heat and work are two transient forms of energy. Let us look at a piston cylinder mechanism (closed system), where high pressure air is filled inside the cylinder fitted with a piston exerting force against some resistance. As the piston moves a distance say l, the work would be done. It can be reduced to the raising of weight by replacing this resisting system by a frictionless pulley and lever such that a weight W is raised, Fig For example, if an electrical battery and resistance is considered as a system, then this system shall do work when electric current flows in an external resistance as this resistance could be replaced by an ideal frictionless motor driving a frictionless pulley and raising a weight. Here, also in reference to work it is obvious that the work is the entity which is available at the boundary of system, thus work can not be stored rather it is energy interaction in transit at the boundary. From the thermodynamic definition of work the sign convention established as positive work shall be the one which is done by the system while the negative work shall be the one that is done upon the system. Figure 9.1 Thermodynamic work 1

2 p-dv Work Figure 9.2 p-dv work for non-flow process Non-flow process is the one in which there is no mass interaction across the system boundaries during the occurrence of the process. Figure 9.2 shows block diagram of a pistoncylinder arrangement in which a constant mass of fluid inside the cylinder is shown to undergo compression. Thus, during compression the type of process shall be non-flow process and the work interaction shall be non-flow work. Say, the force exerted by piston is F, and cross-section area of piston being A, the elemental work done in compressing along the length dl shall be If pressure of fluid is P then F = P A. so dw = P A dl dw = F dl The total work done in piston displacement, from 1 to 2 shall be, 2 2 dw = P A dl dw = P dv 1 1 W = P dv Thus, this is called the non-flow work or displacement work. 1 Thermodynamic processes can be further classified based on the thermodynamic constraints under which they occur. Different types of thermodynamic processes are as detailed below. (i) Constant pressure process or isobaric process: It refers to the thermodynamic process in which there is no change in pressure during the process. Such type of processes are also known as isobaric processes. To understand let us take a cylindrical vessel having gas in it. It has a piston above it. Piston is free to reciprocate in the cylinder. Under normal situation piston shall be subjected to atmospheric pressure. Now, let heat be added to cylinder from bottom of cylinder. Due to heat addition, presuming energy transfer taking place reversibly and system always remaining in equilibrium, the gas shall try to expand. Expansion of gas results in raising up of the piston and it attains a new state say 2. Process is shown on p-v diagram in Fig

3 (ii) Constant volume process or isochoric process: When a fluid undergoes a thermodynamic process in a fixed enclosed space such that the process occurs at constant volume, then the process is called constant volume process or isochoric process. Let us consider heating of a gas in fixed enclosure at constant volume. On p V diagram this process is represented by a vertical line as shown in Fig Area under the process line is zero which indicates that there is rise in pressure but there is no work done as there is no change in volume. Work involved shall be, Figure 9.3 p-dv work for constant volume process From first law of thermodynamics, (iii) Constant temperature process or isothermal process: Thermodynamic process in which the temperature remains constant is called constant temperature or isothermal process. In this case the gas or vapour may be heated at constant temperature and there shall be no change in internal energy. The work done will be equal to the amount of heat supplied, as shown ahead. For a perfect gas during isothermal process; where r = ratio of final and initial volumes. By first law of thermodynamics 3

4 Figure 9.4 p-dv work for isothermal process (v) Polytropic process: Polytropic process is the most commonly used process in practice. In this, the thermodynamic process is said to be governed by the law PVn = constant where n is the index which can vary from to +. Figure 9.5 shows some typical cases in which the value of n is varied and the type of process indicated for different values of n. Thus the various thermodynamics processes discussed above are special cases of polytropic process. Work interaction in case of polytropic process can be given as, (vii) Free Expansion: Free expansion, as the name implies refers to the unrestrained expansion of a gas. Let as take an insulated tank having two compartments separated by a partition, say A and B. Let us assume that compartment A is filled with gas while B is having vacuum. If now the partition is removed and gas allowed to occupy the whole volume of tank, then the gas expands to fill the complete volume space. New pressure of gas will be lesser as compared to initial pressure of gas occupying the compartment A. A close look at the expansion process shows that the expansion due to removal of partition is unresisted expansion due to gas expanding in vacuum. This is also known as free expansion. The reverse of free expansion is impossible and so it is an irreversible process. 4

5 Figure 9.6 p-dv work for free expansion process Others Forms Of Work: Stretching of a wire: Let a wire be stretched by dl due to an application of a force F Work is done on the system. Therefore dw=-fdl Electrical Energy: Flowing in or out is always deemed to be work dw= -EdC= -EIdt Work due to stretching of a liquid film due to surface tension: Let us say a soap film is stretched through an area da dw= -da where is the surface tension. 5