Entropy Change in Isothermal Processes

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Questions and Answers

What is the inlet pressure of the steam entering the turbine?

1.4 MPa

0.5 MPa

450°C

5 MPa (correct)

Which assumption is NOT a part of the analysis of the turbine process?

Kinetic and potential energies are negligible.

There is no heat transfer.

The process is adiabatic.

The process is irreversible. (correct)

What is the outlet pressure of the steam after passing through the turbine?

5 MPa

0.1 MPa

1.4 MPa (correct)

2.5 MPa

Which of the following is a characteristic of the turbine's operational process?

It is a steady-flow process. Signup and view all the answers

What indicates that the turbine process can be considered reversible?

The turbine operates adiabatically. Signup and view all the answers

What is the primary output measured for the turbine's operation?

Work output Signup and view all the answers

What does the differential form of the conservation of energy equation represent for a closed stationary system?

It relates heat and work interactions to internal energy changes. Signup and view all the answers

Which equation is referred to as the first T ds equation or Gibbs equation?

T ds = du + P dv Signup and view all the answers

Which type of work interaction is considered in the Gibbs equation for a simple compressible system?

Boundary work Signup and view all the answers

What does the equation h = u + Pv represent?

The definition of enthalpy Signup and view all the answers

How is the second T ds equation derived?

By eliminating du using the definition of enthalpy Signup and view all the answers

In the context of an internally reversible process, what does dQ int rev equal to?

T dS Signup and view all the answers

What is represented by the symbol 'v' in the equation T ds = dh - v dP?

Specific volume Signup and view all the answers

Which property change does the Gibbs equation explicitly relate to entropy changes?

Internal energy change Signup and view all the answers

What is the change in entropy for the source when 2000 kJ of heat is transferred at 800 K?

-2.5 kJ/K Signup and view all the answers

What is the change in entropy for the sink when 2000 kJ of heat is absorbed at 500 K?

+4.0 kJ/K Signup and view all the answers

What is the total entropy generated during the heat transfer process to the 500 K sink?

1.5 Signup and view all the answers

Which condition leads to a smaller total entropy change in the second part of the calculation?

750 Signup and view all the answers

In the context of the processes described, what is the effect of using a Carnot heat engine?

0 Signup and view all the answers

How can the entropy change of a substance be expressed?

By temperature and pressure Signup and view all the answers

What characterizes the entropy changes measured for the reservoirs in the described process?

Both processes are internally reversible Signup and view all the answers

What does the entropy value of a system depend on?

Its fixed state and properties Signup and view all the answers

What determines the power output of a turbine?

The rate of energy balance Signup and view all the answers

What is the relationship between Ein and Eout for a steady-state turbine?

Ein equals Eout Signup and view all the answers

What is the formula used to calculate the work output of a turbine?

$W_{out} = m(h_{1} - h_{2})$ Signup and view all the answers

What property is NOT provided at the final state of the turbine process?

Temperature Signup and view all the answers

What additional condition is required to find the second property at the final state?

The process is reversible and adiabatic Signup and view all the answers

What assumption about energy transfer is made for the turbine described?

There is no heat transfer (Q = 0) Signup and view all the answers

Which energy forms are considered in the energy balance for the turbine?

Internal energy, kinetic energy, and potential energy Signup and view all the answers

What is implied by the term isentropic in the context of the turbine process?

It refers to constant entropy during the process Signup and view all the answers

What characterizes organized or low-entropy learning?

Creating a solid information network related to existing knowledge. Signup and view all the answers

What happens when students do not secure information properly?

They may experience blackouts during tests. Signup and view all the answers

How can a library be compared to organized learning?

A well-indexed library functions like a well-organized mind. Signup and view all the answers

What is the relationship between entropy and library organization?

Low entropy relates to better information retrieval. Signup and view all the answers

Which library scenario illustrates high entropy?

Books piled chaotically without any order. Signup and view all the answers

Why is a poorly organized library likened to high entropy?

Because it lacks a systematic method to find books. Signup and view all the answers

How do some students mistakenly believe they are learning?

By memorizing information without making connections. Signup and view all the answers

What would typically happen in a high-entropy environment during a retrieval task?

The process of retrieval may be confusing and difficult. Signup and view all the answers

Study Notes

Entropy Change Calculation

Entropy change for reservoirs can be computed during reversible isothermal processes.
For a heat transfer process to a sink at 500 K, the source loses 2000 kJ, resulting in:
- (\Delta S_{source} = -2.5 \text{ kJ/K}) (at 800 K)
- (\Delta S_{sink} = +4.0 \text{ kJ/K}) (at 500 K)
Net entropy generation during the process is +1.5 kJ/K, indicating irreversibility occurs in the partition.
Repeating for a sink at 750 K yields:
- (\Delta S_{source} = -2.5 \text{ kJ/K})
- Total entropy change becomes 0.2 kJ/K, indicating a less irreversible process due to a smaller temperature difference.

Carnot Heat Engine Context

Irreversibilities can be eliminated by using a Carnot heat engine, where total entropy change (\Delta S_{total} = 0).

Entropy Change of Pure Substances

Entropy is a fixed property determined by the state of a simple compressible system, which can be established by two independent intensive properties.
The change in entropy ((s_2 - s_1)) can be expressed through other thermodynamic properties.

Adiabatic Turbine Analysis

Steam enters a turbine at 5 MPa and 450 °C and exits at 1.4 MPa.
The analysis assumes:
- Steady-flow process with no time variation (ΔmCV = 0, ΔECV = 0, ΔSCV = 0).
- Process is reversible and adiabatic with no heat transfer.
Work output is determined using the energy balance equation:
- (\text{Ein} - \text{Eout} = \frac{dE_{system}}{dt} = 0).
- Therefore, net energy transfer equals: (m(h_1 - h_2) = W_{out}).
The process requires both pressure and one additional property for complete specification.

Learning and Organization Analogy

Effective learning is compared to low-entropy organization: well-structured information is easier to retrieve.
A high-entropy scenario, like disorganized books, hampers information retrieval during tests.

Gibbs Equation

The conservation of energy for a closed system undergoing internally reversible processes is given by: [dQ_{int , rev} - dW_{int , rev, out} = dU.]
Relating heat and work:
- (dQ_{int , rev} = T dS) and (dW_{int , rev, out} = P dV).
This leads to the Gibbs equation: [T dS = dU + P dV]
Only boundary work is notable for simple compressible systems during reversible processes.

Enthalpy Relationship

The second T ds equation is expressed using the definition of enthalpy (h = u + Pv):
- (\int T ds = dh - v dP).
Both equations are significant for relating changes in entropy to alterations in other thermodynamic properties.

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Description

This quiz explores the calculations of entropy change during reversible isothermal processes, particularly focusing on heat transfer to reservoirs at specified temperatures. Understand the impact of heat loss from the source and the resulting changes in entropy for both the source and sink in thermodynamic systems.