![]() The differential work is, therefore, dW = - p ext( yzdx + xzdy + xydz), provided the external pressure is the same on all faces of the box. Here, A x ≈ yz, A y ≈ xz, and A z ≈ xy, where the differential cross terms are neglected. ![]() This equation applies to any arbitrarily shaped system.įor example, consider a rectangular box that expands differentially into the surroundings on three sides, as illustrated in Fig. The expression for the differential work can be simplified further as, where nV is the total volume and V is the molar volume (volume/mole). The minus sign indicates that work is positive if the displacement is negative (i.e., an external force compresses the system). A x is the area normal to the x -coordinate that is being displaced, and so forth. In Cartesian coordinates, dW = - p ext( A x dx + A y dy + A z dz), where the external pressure is constant along the boundary of the system. For expansion/compression work, the external force is equal to an external pressure supplied by the surroundings multiplied by the corresponding area along the boundary of the system. Thus, the differential mechanical work that results from a differential displacement is given by. From physics, work is performed whenever a force acts over a distance. The two types of work considered are expansion/compression work and flow work (assumption three). Where the left side refers to energy within the system and the right side to energy that flows across the system boundaries into the system. Compression (or expansion) of the system boundaries causes work on the system denoted by Ẇ. The rate of heat flow from the surroundings across the system boundaries into the system is given by. Based on assumption one, there is only one molar flow rate into the system. Because we neglect potential and kinetic energy of the mass that flows into the system (assumption two), the energy associated with the mass influx into the system is simply Uṅ, where ṅ is the molar flow rate. 1 contains three terms: mass influx into the system that carries energy heat transfer into the system and compression work done by the surroundings on the system. 2 shows that when work or heat is added to the system, the molecular activity increases, causing the total internal energy to increase that is. The property, U, is the molar internal energy (total energy/mole). With this definition, a total macroscopic energy balance in the system, at an instantaneous point in time, givesĪnd n U, the total internal energy, is equal to the total energy within the system by assumption four previously discussed. ![]() The microscopic kinetic energy is sometimes called thermal energy, which is proportional to temperature. Internal energy of a substance is the sum of the potential energy arising from chemical bonds of atoms and electrons and the sum of the kinetic energy of the atoms and molecules. M indicates mass, and Q indicates heat.īefore proceeding, we must define internal energy. 1 – Three types of thermodynamic systems. Heat transfer is positive when heat is exchanged from the surroundings to the system.įig. ![]() Energy in the form of heat might enter or leave the system across the system boundaries.We neglect potential energy and kinetic energy changes within the system.The mass that enters or exits the system also does work-sometimes called flow work or pressure work. Work is positive when the surroundings do work on the system (i.e., the system contracts). Thus, work can be done by the system on the surroundings or vice versa. The boundaries of the system can expand or contract. The only types of work that are present are expansion/compression of the system and flow work.This is often a good assumption when the fluid is not moving near the speed of sound, the change in height over the system is not large, or the system temperature variations are not large. We neglect kinetic and potential energy carried by the mass. Mass can carry internal energy into or out of the system.The mass flow rate into the system is positive, whereas flow rates out of the system to the surroundings are negative. Mass flows into or out of the system along one boundary of the system.We make the following assumptions and definitions: 1, an open system allows mass and energy to flow into or out of the system. We begin with the first law of thermodynamics applied to an open thermodynamic system.
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