Air flows steadily between two sections in a duct. At...

Air flows steadily between two sections in a duct. At section $(1),$ the temperature and pressure are $T_{1}=80^{\circ} \mathrm{C}, p_{1}=301$ $\mathrm{kPa}(\mathrm{abs}),$ and at section $(2),$ the temperature and pressure are $T_{2}=180^{\circ} \mathrm{C}, p_{2}=181 \mathrm{kPa}(\mathrm{abs}) .$ Calculate the (a) change in internal energy between sections (1) and $(2),(\mathbf{b})$ change in enthalpy between sections (1) and $(2),(\mathrm{c})$ change in density between sections (1) and $(2),(\mathbf{d})$ change in entropy between sections (1) and (2). How would you estimate the loss of available energy between the two sections of this flow?

Air flows steadily between two sections in a duct. At section $(1),$ the temperature and pressure are $T_{1}=80^{\circ} \mathrm{C}, p_{1}=301$ $\mathrm{kPa}(\mathrm{abs}),$ and at section $(2),$ the temperature and pressure are $T_{2}=180^{\circ} \mathrm{C}, p_{2}=181 \mathrm{kPa}(\mathrm{abs}) .$ Calculate the (a) change in internal energy between sections (1) and $(2),(\mathbf{b})$ change in enthalpy between sections (1) and $(2),(\mathrm{c})$ change in density between sections (1) and $(2),(\mathbf{d})$ change in entropy between sections (1) and
(2). How would you estimate the loss of available energy between the two sections of this flow?

Key Concepts

Internal Energy

Internal energy is a thermodynamic property that reflects the total energy contained within a system due to the random motion of molecules. For ideal gases, the change in internal energy depends solely on the temperature change and the specific heat at constant volume (cv), without direct dependence on pressure. This concept is essential in analyzing energy transformations in flowing systems.

Enthalpy

Enthalpy represents the total heat content of a system, combining its internal energy with the product of pressure and volume. In processes at constant pressure, such as many flow systems, the change in enthalpy is directly related to the specific heat at constant pressure (cp) and the temperature change. This property is a key measure when evaluating energy transfer in ducts or open systems.

Density

Density is the mass per unit volume of a substance and is a fundamental property that can be determined for an ideal gas using the ideal gas law. The relationship, expressed as ? = p/(RT) where p is pressure, R is the specific gas constant, and T is the absolute temperature, highlights how changes in temperature and pressure affect the mass distribution within a system.

Entropy

Entropy is a measure of the disorder or randomness in a system and is central to the second law of thermodynamics. For ideal gases, changes in entropy during a process can be computed using relations that involve temperature and pressure variations. This concept is crucial for understanding the irreversibility and efficiency losses in thermodynamic processes.

Exergy

Exergy, or available energy, is a measure of the maximum useful work possible during a process that brings the system into equilibrium with a reference environment. It accounts for the losses due to irreversibilities such as friction or heat transfer. Estimating the loss of available energy involves analyzing the changes in state properties and comparing the actual process with an ideal reversible process, thereby quantifying the efficiency loss in the flow.

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