Heat is the energy transferred between two parcels of different temperature and the heat received by the system is dQ = mcdT

where m is the mass of a parcel, c is the specific heat, and dT is the temperature change.

First law of thermodynamics

The total amount of energy of a system is conserved. This law can be written in a differential form dE = dQ + dW (2.23)

i.e., the change in internal energy, dE, of the system is equal to the heat received by the system plus the work done to the system.

2.3.3 Entropy

Reversible processes and irreversible processes

A reversible process is one in which the system is very close to its equilibrium at all times, so that the process can be reversed with no changes in the system and its environment. In an irreversible process, the system moves away from the equilibrium state, so that the system and its environment cannot come back to their initial states. The adjective "irreversible" does not mean that the system cannot come back to its initial state; all it means is that some irreversible changes must occur in the environment if the system is to be brought back to its initial state.

Change of entropy

Entropy is an essential thermodynamic variable of a system, which was introduced in the study of thermodynamics of irreversible processes. Change of entropy of a system is defined as dn > dq/T

where the equal sign is valid for reversible processes only, and dq is the heat received by the system. For irreversible processes there is an additional increase of entropy, as indicated by the "greater than" sign. For a reversible process, the system and its environment remain unchanged after a complete cycle, i.e., dn = / W™^ = 0 (2.25)

Although calculating entropy for an ideal gas is quite easy, the calculation of seawater entropy was not easy because there was no simple and reliable formula. However, standard formulae are now available. Accordingly, entropy is defined as a thermodynamic state variable of seawater, and for given temperature, salinity and pressure, entropy can be calculated from standard formulae, as discussed later in this section.

2.3.4 The second law of thermodynamics

Entropy change of a system due to heat exchange with the environment must obey d n > dq/T.

The equals sign is valid only for reversible processes. In general cases, the inequality applies, i.e., the total entropy of the system and its environment increases due to irreversible processes.

Clausius inequality: The total entropy of an isolated system cannot decrease, i.e., A-ntotai > 0. By definition, an isolated system includes the system and its environment.

The Carnot cycle

In order to extract the maximal work from a heat source, an idealized cycle, called the Carnot cycle, based on one kilogram of ideal gas, is designed as follows (Fig. 2.3). An imaginary perfect engine works between a heat source at temperature Ti and a cooling source at temperature T2 < T1. The equation of state for one kilogram of ideal gas is

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