The First Law of Thermodynamics for a System

For a system undergoing a thermod)mamic cycle, the first law of thermodynamics is given as 

It physically states that the cyclic integral or the sum of heat transfer in all processes is equal to fhe cyclic integral or the sum of work done in all 

The first law of thermodynamics for a specific process states that the change in energy content of a system is caused by net transfer of energy in fhe form of heat and work across the system boundary and given as 

U = internal energy associated with rotational, vibrational, and translational motions and structures of the atoms and molecules 

With the substitution of the expressions for different energy forms. Equation 3.15 can be written as 

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The combination of the Clausius inequality (eq. 1.30) and the first law of thermodynamics for a system at constant volume thus gives... 

Cooling curves such as the two in Figure 8.7 were determined for constant enthalpy (or Joule-Thomson) expansions, obtained from the First Law of Thermodynamics for a system flowing at steady-state, neglecting kinetic and potential energy changes ... 

This text is an introduction to engineering heat transfer. The philosophy of the text is based on the development of an inductive approach, earlier introduced by the author ( Conduction Heat Transfer, 1966), to the formulation and solntion of applied problems. Since the greatest difficulty a student faces is how to formulate rather than how to solve a problem, the formulation of problems is stressed from the beginning and throughout the entire text. This is done by first noting that heat transfer rests on but goes beyond thermodynamics, and taking as a basis the well-known form of the first law of thermodynamics for a system,... 

For a pure substance at rest with no electrical or magnetic effects, the first law of thermodynamics for a closed system is expressed for a differential change as... 

The first law of thermodynamics for open systems applies the transport of work dl heat dQ mass dm, with its enthalpy h and external energy (kinetic and potential energy) across the system boundaries equals the change in internal energy dtJ and external energy d a in the system. 

The first law of thermodynamics for a closed system (which we will generally refer to as the energy balance) between two instants of time is... 

Equation (4.23) is known as the first law of thermodynamics for a closed system.] Keep in mind that a system may do work, or have work done on it, without some obvious mechanical device such as a pump, shaft, and so on, being present. Often the nature of the work is implied rather than explicity stated. For example, a cylinder filled with gas enclosed by a movable piston implies that the surrounding atmosphere can do work on the piston or the reverse a batch fuel cell does no mechanical work, unless it produces bubbles, but does deliver a current at a potential difference electromagnetic radiation can impinge on or leave a system and so forth. 

This relation is recognized from introductory subjects on thermodynamics. Recall that in equilibrium thermodynamics a local formulation is generally not needed, since the intensive state variables are independent of the space coordinates. This fundamental formulation of the total energy balance is known as the first law of thermodynamics for a closed system, which expresses the fundamental physical principle that the total energy of the system, Etotab is conserved (a postulate). 

Consider part of a shell of constant wall thickness as shown in Fig. 2.1. Let the inner and outer surface temperatures be 7) and, respectively, and the thickness of the shell be t = X2 — i- Following the five-step formulation, we assume first a differential system (Step 1). The first law of thermodynamics for this system (Step 2) yields... 

Assuming the plate temperature to be uniform, consider a system for the entire plate. The first law of thermodynamics for this system is... 

In practice, pure-component molar enthalpies are employed to approximate A/7rx. This approximation is exact for ideal solutions only, when partial molar properties reduce to pure-component molar properties. In general, one accounts for more than the making and breaking of chemical bonds in (3-35). Nonidealities such as heats of solution and ionic interactions are also accounted for when partial molar enthalpies are employed. Now, the first law of thermodynamics for open systems, which contains the total differential of specific enthalpy, is written in a form that allows one to calculate temperature profiles in a tubular reactor ... 

One interesting feature of the differential form of the first law of thermodynamics for a pure material which does not exchange mass with its surroundings (i.e., a closed system) is that an exact differential (i.e., dU) is equal to the sum of two path-dependent inexact differentials heat input to the system (dq) and work performed on the system (dw) ... 

The heat associated with a specific polymerization reaction depends on the temperatures of both the monomers and polymer. A standard basis that is consistent for treating polymerization heat effects results when the products of polymerization and the monomers are all at the same temperature. Consider a calorimeter method of measurements of heat of polymerization of monomers. The initiator is mixed with the monomer, and the system is a continuous flow CSTR. The polymerization reactions take place in the CSTR. The polymerization products enter a devolatilizer where the monomers are vaporized and removed from the product mix and recycled back to the reactors. The CSTR is water cooled to bring the monomers/polymer to the reactor temperature. There is no shaft work performed by the process. The CSTR is built, so that changes in potential and kinetic energy are negligible. The first law of thermodynamics for open systems can be written for the system as... 

In formulating the first law of thermodynamics in Section 2.1 we tacitly assumed that the only external work that a system can do is the work of expansion (p da). However, a system may also perform external work by other means (e.g., chemical or electrical). Therefore, in general, the first law of thermodynamics for a unit mass of a system should be written as... 

Notice that Eq. (59) is fully compatible with Eq. (52) and with (21). However, it is important to stress that Eq. (59) is exact and a natural consequence of the first law of thermodynamics for open systems. 

The basic underlying principle governing such systems is the First Law of Thermodynamics for a control volume or open system. In Chapter 2, this approach was used to develop the Bernoulli balance used with macroscopic fluid mechanics systems. Here we will use a different form hut one that nonetheless emanates from the First Law. 

The first law of thermodynamics for a reacting system under SSSF process with negligible changes in kinetic energy and potential energy is given as... 

Maximum Electrical Work for a Reversible Process Consider a generic reversible system with mechanical and electrical work and heat transfer at constant temperature. From the first law of thermodynamics for a simple compressible system... 

In other words, the change in the internal energy of the system is strictly related to the amount of energy that is added to the system by heat transfer or mechanical work. Often, one will use the symbol A to describe the difference between two points, in which case the first law of thermodynamics for a closed system is written as... 

The first law of thermodynamics for an isolated system can be stated as follows There exists a function of the state of a uniform phase called the energy which is conserved for... 

The first law of thermodynamics provides a description of the energy balance for a given process the second law provides a criterion for deciding whether or not the process will occur spontaneously. The second law of thermodynamics defines the entropy change (A5, in units of J K l) associated with a change in a closed system in terms of the heat absorbed by the system at constant temperature T ... 

The temperature field can be obtained by solving a partial differential equation, the so called heat conduction equation, which will be derived now. This requires the application of the first law of thermodynamics to a closed system, namely a coherent region of any size, imaginarily taken from the conductive body, Fig. 2.1. The volume of this region is V and it has a surface area A. The first law produces the following power balance for the region ... 

Let s apply the first law of thermodynamics to a closed system (i.e. a system that can exchange heat and work with its surroundings, but not matter). The first law for a closed system can be written as... 

Now consider a closed system that can alter its volume V. In this case, the work performed by the system is 5FK = pdY- Combining the first and the second laws of thermodynamics for a closed system (i.e. inserting the inequality in Eq. (1.2) into Eq. (1.1)), we obtain... 

The first law of thermodynamics is a formulation of the principle of conservation of energy. It states that the increase in the internal energy of a system equals the heat absorbed by the system from its surroundings minus the work done by the system on its surroundings. For infinitesimal changes, the first law is expressed mathematically by the equation... 

Since the well-known familiar forms of general principles have been deduced and always written for a system, consider first a system coinciding with the control volume at the final state while including in the initial state the piston-cylinder assembly as well as the control volume. Let E, E2 and E, E"v denote the initial and final values of the total energy of the system and the control volume, respectively. The first law of thermodynamics for the system undergoing a differential process is2... 

Now, consider an enclosure filled with monochromatic radiation Ga, and place a monochromatically opaque (r =0) body into this enclosure (Fig. 8.12). Let the monochromatic reflectivity and emissive power of the body be pi and Fa, respectively. Under equilibrium, the first law of thermodynamics for the system enclosing the body gives... 

The first law of thermodynamics for an open system at steady state that performs no work on the surroundings other than pV work across the inlet and outlet planes of a differential control volume is written with units of energy per volume per time ... 

For a system undergoing a cycle, the net heat transfer is equal to the net work done. There is no change in its internal energy as the system returns to its initial state. Mathematically, first law of thermodynamics for a cycle is given by (Domkundwar et al. 1985 Nag 2010),... 

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