Representation of Various Processes on T-S Chart : Now to derive the equations for change of entropy during,ĩ. Change in Entropy during Various Processes : Now consider a unit mass of a gas which changes its states from pressure P 1, specific volume v 1 and temperature T 1 to a new state P 2, V 2, T 2.Ĩ. We know that, the first law applied to a closed system undergoing a process gives, General Equations for Change in Entropy : Property Relations from Energy Equations :įor deriving the equation for change of entropy it is essential to know equation based on I and II law of thermodynamics.ħ. The reverse occurs when heat is removed from the system.Ħ. When heat is supplied to the system, the disorderly motion of molecules increases and so the entropy of the system increases. It may be stated roughly that “The entropy of a system is a measure of the degree of molecular disorder existing in the system”. So there is a close link between entropy and disorder. And an isolate system always tends to a state of greater entropy. It is a tendency on the part of nature to proceed to a state of greatest disorder. Thus an irreversible process always tends to take the system (isolated) to state of greater disorder. The reason is obvious, as the mixing process is irreversible and irreversible process is always associated with the increase in entropy. of the system remains the same, but we find that the entropy increase. If we assume that initially both gases have the same volume and temperature then after removing the partition each gas occupies double the previous volume while the temperature and the I.E. When the partition or barrier is removed, the molecules of both gages get more space to move randomly and therefore collision take place between the mole molecules of the same gas as well as of both the gases, and after some time, equilibrium will be established. We know that all natural processes are irreversible processes and during irreversible processes entropy increases and hence entropy of the universe always increases.Ĭonsider an isolated system comprising of two gases O 2 and H 2 in a separated box as shown in Fig. This is known as the Principle of increase of entropy. Since for an isolated system δQ = 0, from equation,Įquation (2) states, that entropy of an isolated system either increases or remains constant and never decreases. Hence according to the first law of thermodynamics, the IE of the system will remain constant. We know that, in an isolated system, matter, work or heat cannot cross the boundary of the system. The effect of irreversibility is always to increase the entropy of the system.Ĭhange of Entropy for an Isolated System : Where equality sign is for reversible process and inequality sign is for an Irreversible process (from Eq. Since cyclic integral of any property is zero and entropy is a property we can write, Now to find the value of change in entropy in an Irreversible process.Ĭonsider a system, which change its state from state point (1) to state point (2) by following the reversible path a and returns from state point (2) to state point (1) by following the irreversible path b as shown in Fig. We know that, change in entropy for a reversible process is given by, It implies whether any cyclic process is reversible or irreversible or impossible.Ĭhange of Entropy in an Irreversible Process : Thus expression is known as Clausius Inequality. The magnitude of δQ/T (i.e., dS) is same for the paths a and b and it does not depend upon the end states, hence it is point function and we know that properties are point-functions, hence it is a property of the system. The above integral may be replaced as the sum of two integrals one for the path a and other for the path b. May be read as integral for the reversible path 1 – a 2 – b – 1. Then the two paths 1- a – 2 and 2 – b -1 together will form a cycle. Then, we will able to say that, entropy is a property of the system.Ĭonsider a system which changes its state from state point (1) to state point (2) by following the reversible path a and returns from state point (2) to state point (1) by following the reversible path b. To prove this, we have to prove that the change of entropy does not depend upon path but it depends upon end states. Analysis of second law will lead to the definition of another derived property known as Entropy.
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