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Chapter 5: Problem 12

A hot combustion gas enters a turbine operating at steady state and expands adiabatically to a lower pressure. Would you expect the power output to be greater in an internally reversible expansion or an actual expansion?

Short Answer

Expert verified
The power output is greater in an internally reversible expansion due to minimized energy losses.

Step by step solution

01

Understand the Given Scenario

Identify that the problem involves a hot combustion gas entering a turbine and expanding adiabatically to lower pressure. The goal is to compare the power output between an internally reversible expansion and an actual expansion.
02

Define Adiabatic Process

Adiabatic expansion means no heat transfer occurs during the process. Hence, the change in energy is entirely due to work done by the gas.
03

Internally Reversible vs. Actual Expansion

In an internally reversible process, the system changes state in such a way that the process can be reversed without leaving any change in the system or surroundings. In a real scenario, there are irreversibilities due to friction, turbulence, etc.
04

Compare Power Output

In an internally reversible adiabatic (isentropic) expansion, the entropy remains constant, and the process is more efficient compared to an actual expansion with irreversibilities. Therefore, the power output is higher in an internally reversible expansion as there are no losses.
05

Conclusion

Since an internally reversible process maximizes the work output by minimizing energy losses, the power output in an internally reversible expansion would be greater than in an actual expansion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Internally Reversible Process
An internally reversible process is an idealized concept in thermodynamics. In such a process, the system transitions between states in a manner that can be completely reversed without leaving any changes in the system or its surroundings. This means there are no dissipative effects like friction, turbulence, or non-equilibrium phenomena. When dealing with turbines, an internally reversible process is used as a benchmark because it represents the maximum efficiency scenario. In reality, most processes have some irreversibilities due to factors such as mechanical friction or fluid turbulence that reduce their efficiency.
Isentropic Expansion
Isentropic expansion is a specific type of internally reversible process where entropy remains constant. Entropy is a measure of disorder in a system, and during isentropic expansion, there is no increase in entropy, implying that the process is highly efficient. For turbines operating adiabatically (without heat transfer), isentropic expansion is ideal because it results in maximum work output.
This can be formulated as:
鉂� 鉂� h_{1} - h_{2} = W_{out} - 鉂� where 饾悺_饾悳_ is the enthalpy at state 1 and h_2 is the enthalpy at state 2. 鉂� 鉂� By achieving isentropic expansion, turbines can potentially realize their highest possible efficiency.
Thermodynamic Efficiency
Thermodynamic efficiency compares the amount of work or energy a system produces to the energy input. It is a measure of how well the system converts energy from one form to another. For turbines, efficiency is key to determining performance. Internally reversible processes, such as isentropic expansions, often provide a benchmark for efficiency. While real turbines can't achieve 100% efficiency due to unavoidable irreversibilities, designing as close as possible to the internally reversible process helps. The higher the efficiency, the less energy is wasted, resulting in higher work output and better performance.
Power Output Comparison
When comparing power output in turbines, it's crucial to consider both internally reversible and actual processes. In an ideal internally reversible (isentropic) expansion, power output is maximized since there are no energy losses. However, in actual expansion, losses due to irreversibilities like friction or turbulence reduce the power output.
The conclusion is that an internally reversible expansion will always produce greater power output compared to an actual expansion. This is because the internally reversible process operates with optimal efficiency.
Understanding this comparison helps in designing more efficient turbines and improving power generation systems overall.

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Most popular questions from this chapter

Using the Kelvin-Planck statement of the second law of thermodynamics, demonstrate the following corollaries: (a) The coefficient of performance of an irreversible refrigeration cycle is always less than the coefficient of performance of a reversible refrigeration cycle when both exchange energy by heat transfer with the same two reservoirs. (b) All reversible refrigeration cycles operating between the same two reservoirs have the same coefficient of performance. (c) The coefficient of performance of an irreversible heat pump cycle is always less than the coefficient of performance of a reversible heat pump cycle when both exchange energy by heat transfer with the same two reservoirs. (d) All reversible heat pump cycles operating between the same two reservoirs have the same coefficient of performance.

Two reversible refrigeration cycles are arranged in series. The first cycle receives energy by heat transfer from a cold reservoir at temperature \(T_{C}\) and rejects energy by heat transfer to a reservoir at an intermediate temperature \(T\), greater than \(T_{C .}\) The second cycle receives energy by heat transfer from the reservoir at temperature \(T\) and rejects energy by heat transfer to a higher-temperature reservoir at \(T_{\mathrm{H}}\). Obtain an expression for the coefficient of performance of a single reversible refrigeration cycle operating directly between cold and hot reservoirs at \(T_{\mathrm{C}}\) and \(T_{\mathrm{H}}\), respectively, in terms of the coefficients of performance of the two cycles.

Answer the following true or false. (a) A process that violates the second law of thermodynamics violates the first law of thermodynamics. (b) When a net amount of work is done on a closed system undergoing an internally reversible process, a net heat transfer of energy from the system also occurs. (c) A closed system can experience an increase in entropy only when a net amount of entropy is transferred into the system. 5.3 Answer the following true or false. (a) A process that violates the second law of thermodynamics violates the first law of thermodynamics. (b) When a net amount of work is done on a closed system undergoing an internally reversible process, a net heat transfer of energy from the system also occurs. (c) A closed system can experience an increase in entropy only when a net amount of entropy is transferred into the system.

\(5.54 \mathrm{~A}\) heat pump maintains a dwelling at temperature \(T\) when the outside temperature averages \(5^{\circ} \mathrm{C}\). The heat transfer rate through the walls and roof is \(2000 \mathrm{~kJ} / \mathrm{h}\) per degree of temperature difference between the inside and outside. If electricity costs 8 cents per \(\mathrm{kW} \cdot \mathrm{h}\) (a) determine the minimum theoretical operating cost for each day of operation when \(T=20^{\circ} \mathrm{C}\). (b) plot the minimum theoretical operating cost for each day of operation as a function of \(T\) ranging from 18 to \(23^{\circ} \mathrm{C}\).

At steady state, a new power cycle is claimed by its inventor to develop power at a rate of \(65 \mathrm{~kW}\) for a heat addition rate of \(4.5 \times 10^{5} \mathrm{~kJ} / \mathrm{h}\), while operating between hot and cold reservoirs at 800 and \(400 \mathrm{~K}\), respectively. Evaluate this claim.
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