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### Derive the Entropy of Real Gases

Entropy of real gases: We know that: (∂S / ∂P)T = - (∂V / ∂T)P ……………………. (1) is one of the Maxwell relations which can also be written as: dS – (∂V / ∂T) P) dP …………………. (2) Integrating between pressure P1 and P2 at constant tempearute T , we ...

### Determine the Absolute Entropies of Solids

Absolute entropies of solids: Entropy change for an infinitesimally small change of a state of a substance is given as: dS = dq / T If the changes take place at constant pressure, then, (∂S) P = (∂q) P / T Multiplying both the sides by ∂T, we will ...

### Define the Nernst Heat Theorem

The Nernst Heat Theorem Let us consider the Gibbs-Helmholtz equation which includes chemical reaction i.e.: ∆G - ∆H = T (∂ (∆G)/∂T) P ………………………………….. (1) Where ∆G -------> change in free energy ∆H -------> ...

### What is irreversible process? Give an example of irreversible process.

Irreversible process: An Irreversible process is one in which heat is transferred through a finite temperature. Irreversible process is also known as spontaneous process because these processes take place at very fast rate. Examples of irreversible processes are as follows: 1) Relative motion with friction 2) Falling of the water from ...

### Define third law of thermodynamics. Discuss the importance of third law of thermodynamics.

The third law of thermodynamics states that: “The entropy of all the perfect crystalline solids is zeros at absolute zero temperature”. The third law of thermodynamics is also referred to as Nernst law. It provides the basis for the calculation of absolute entropies of the substances. Mathematically, LimT ...

### A mass ‘m’ of fluid at temperature T1 is mixed with an equal amount of the same fluid at temperature T2. Prove that the resultant change of entropy of the universe is: [2 mc ln (T1 + T2) / 2]/[(T1 T2)1/2]and also prove that it is always positive.

Mean temperature of the mixture = (T1 + T2) / 2 Thus change in entropy is given by: ∆S = S2 - S1) = mc (T1 + T2)/2∫ T1 (dT / T) – mc T2∫ T1 + T2)/2 (dT / T) = mc ln (T1 + T2)/2 ...

### Derive the Gibbs-Duhem Equation and give its Applications?

Gibbs-Duhem Equation The Gibbs free energy can be defined in two different ways once by subtracting off combinations of entropy S, enthalpy H and temperature T and other as a sum of chemical potentials and amounts of species. The fact that they are equal gives a ...

### Explain Clapeyron-Clausius Equation and also give its derivation

Clapeyron discovered an important fundamental equation which helps in finding the extensive application in one component, two phase system and by Clausius from second law of thermodynamics. Hence this fundamental equation is known as Clapeyron-Clausius Equation. One of the uses of this equation is to ...

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