Heat, Work, and the First Law

The heat and work appearing in the first law are two different modes of energy transfer. They can be defined in a general way as follows. 

Heat refers to the transfer of energy across the boundary caused by a temperature gradient at the boundary. 

Work refers to the transfer of energy across the boundary caused by the displacement of a macroscopic portion of the system on which the surroundings exert a force, or because of other kinds of concerted, directed movement of entities (e.g., electrons) on which an external force is exerted. 

An infinitesimal quantity of energy transferred as heat at a surface element of the boundary is written dq, and a finite quantity is written q (Sec. 2.5). To obtain the total finite heat for a process from q = fdq (Eq. 2.5.3), we must integrate over the total boundary surface and the entire path of the process. 

An infinitesimal quantity of work is dw, and a finite quantity isw=f din. To obtain w for a process, we integrate all kinds of work over the entire path of the process. 

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Carnot s principle in Kelvin form (4.19) makes clear that the usefulness of a certain quantity of heat energy q depends on its temperature. Thus, a quantity of high-7" heat intrinsically carries greater work capacity than the equivalent quantity of low-7" heat. Even if the first law tells us that a quantity of heat q and work w are energetically equivalent, the second law restricts what fraction can actually be extracted from q as useful work, depending on its temperature. 

Energy can be transferred to (or from) a chemical system from (or to) the surroundings in the form of heat q or work w. The first law of thermodynamics states that the change in the system s internal energy E is equal to the sum of the heat and work inputs (or outputs) ... 

Suppose any closed system (thus having a constant mass) undergoes a process by which it passes from an initial state to a final state. If the only interaction with its surroundings is in the form of transfers of heat, Q, and work, W, then only the internal energy, U, can be changed, and the First Law of Thermodynamics is expressed mathematically as... 

In a reversible adiabatic expansion with expansion work only, the heat is zero and the first law becomes... 

Comparing Equation 3.82 and the first law equation for reacting system with no work, we can see that enthalpy of combushon is equivalent to the heat transfer rate across the control volume surrounding the combustion chamber. 

The first law of thennodynamics relates the energy change m a system at constant volume to the work done on the system and the heat added to the system q. 

The first law of thermodynamics - which is just a statement of energy conservation - allows us to find out how much work is produced by all the changes in N, all the changes in U, and all the heat flows, from the equation... 

It follows directly from the first law of thermodynamics that if a quantity of heat Q is absorbed by a body then part of that heat will do work W and part will be aecounted for by a rise in the internal energy AE of that body, i.e. 

The First Law Heat, Work, and Other Forms of Energy... 

The second part of the first law of thermodynamics arises when the requirement that the process be adiabatic is dropped recall that this means the system is not insulated, and processes can be caused by heating and cooling. In a general process (the only assumption is that matter is not added or removed from the system), if an amount of work W is done on the system and the energy changes by DE then the heat supplied to the system Q is defined by... 

The first law of thermodynamics goes a step further. Taking account of the fact that there are two kinds of energy, heat and work, the first law states ... 

In applying the first law, note (Figure 8.10, p. 215) that q and w are positive when heat or work enters the system from the surroundings. If the transfer is in the opposite direction, from system to surroundings, q and w are negative. 

Now if the chemical reaction had been allowed to proceed without the performance of any external electrical work, say in a calorimeter, so that the initial and final temperatures of the system are both T, the change of intrinsic energy would have been the same as that occurring in the process described above, as we know from the First Law. Thus the heat of reaction, Q will be equal to the increase of intrinsic energy ... 

The first law is one of conservation of mass and energy, whereby a balance exists between energy, work, and heat quantities. The second law relates to energy flow, whereby heat can only flow from a hotter body to a colder one. 

Equation (2.38) relates an entropy change to the flow of an infinitesimal quantity of heat in a reversible process. Earlier in this chapter, we have shown that in the reversible process, the flow of work 6 ir is a minimum for the reversible process.51 Since ir and q are related through the first law expression... 

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