Derivation of the expression for exergy

[Mohankpvk]

I am using the book 'Fundamentals of thermodynamics' by Moran et al., In the exergy chapter, while deriving the expression for exergy ,a term representing the entropy generation in the combined system is neglected.Then the resulting expression is said to be the expression for exergy.But that entropy generation term can be zero only if the system and the environment(within the combined system) are at the same temperature.But even for system at a different temperature,the term is neglected.Are they deliberately neglecting the irreversibilities(to calculate max possible work) or am I not understanding it rightly?

 

[Andrew Mason]

I am using the book 'Fundamentals of thermodynamics' by Moran et al., In the exergy chapter, while deriving the expression for exergy ,a term representing the entropy generation in the combined system is neglected.Then the resulting expression is said to be the expression for exergy.But that entropy generation term can be zero only if the system and the environment(within the combined system) are at the same temperature.But even for system at a different temperature,the term is neglected.Are they deliberately neglecting the irreversibilities(to calculate max possible work) or am I not understanding it rightly?

Entropy generation can be zero if the system and it surroundings are at different temperatures, provided heat flow occurs between the surroundings (a reservoir) and the system at arbitrarily small temperature differences. For example, a Carnot engine operates between hot and cold reservoirs but heat transfer occurs between the system and reservoirs over infinitesimal temperature differences. Obtaining the maximum thermodynamic work from a system in moving between two states must necessarily involve a process in which heat flow occurs. Otherwise, there could be no work done at all.

 

[Mohankpvk]

Entropy generation can be zero if the system and it surroundings are at different temperatures, provided heat flow occurs between the surroundings (a reservoir) and the system at arbitrarily small temperature differences. For example, a Carnot engine operates between hot and cold reservoirs but heat transfer occurs between the system and reservoirs over infinitesimal temperature differences. Obtaining the maximum thermodynamic work from a system in moving between two states must necessarily involve a process in which heat flow occurs. Otherwise, there could be no work done at all.

Thank you for answering.So, to generate work, an engine cycle should be used to transfer heat between the system(at a higher state) and the environment(at ground state).If Carnot cycle is used, the net change in entropy of the combined system will be zero(at the end of complete cycle i.e. in case of carnot even at the end of a heat transfer process).So the entropy term can be zero(this case will give the max work).Is this right?

 

[Chestermiller]

I am using the book 'Fundamentals of thermodynamics' by Moran et al., In the exergy chapter, while deriving the expression for exergy ,a term representing the entropy generation in the combined system is neglected.Then the resulting expression is said to be the expression for exergy.But that entropy generation term can be zero only if the system and the environment(within the combined system) are at the same temperature.But even for system at a different temperature,the term is neglected.Are they deliberately neglecting the irreversibilities(to calculate max possible work) or am I not understanding it rightly?

Even if the system is at a different temperature from the surroundings, the process can still be carried out reversibly if you have an ideal Carnot engine operating between the system temperature and surroundings temperature, such that, if the system is at a higher temperature than the surroundings, for example, the low temperature leg of the Carnot cycle is carried out at the surroundings temperature. As time progresses, and the system temperature becomes lower, you replace the original Carnot engine with a new one operating between the new system temperature and the same surroundings temperature. You continue doing this game plan until the system temperature has finally reached the surroundings temperature.

The exergy is basically the maximum amount of non-PV work you can obtain from a system operating in contact with an ideal reservoir at a constant environmental temperature and a surroundings at a constant environmental pressure. All heat transfer and all PV work are done using this idealized environment. Even though PV work also occurs within the Carnot engine, the working gas in the Carnot engine is not considered part of the surroundings, but part of the system, so the Carnot engine work is not considered exchange of PV work with the surroundings. It is thus part of the exergy.

 

[Mohankpvk]

Even if the system is at a different temperature from the surroundings, the process can still be carried out reversibly if you have an ideal Carnot engine operating between the system temperature and surroundings temperature, such that, if the system is at a higher temperature than the surroundings, for example, the low temperature leg of the Carnot cycle is carried out at the surroundings temperature. As time progresses, and the system temperature becomes lower, you replace the original Carnot engine with a new one operating between the new system temperature and the same surroundings temperature. You continue doing this game plan until the system temperature has finally reached the surroundings temperature.

The exergy is basically the maximum amount of non-PV work you can obtain from a system operating in contact with an ideal reservoir at a constant environmental temperature and a surroundings at a constant environmental pressure. All heat transfer and all PV work are done using this idealized environment. Even though PV work also occurs within the Carnot engine, the working gas in the Carnot engine is not considered part of the surroundings, but part of the system, so the Carnot engine work is not considered exchange of PV work with the surroundings. It is thus part of the exergy.

Thank you.Nice answer.