Using the tables for water, determine the specified property...

Using the tables for water, determine the specified property data at the indicated states. Check the results using $I T$. In each case, locate the state by hand on sketches of the $p-v$ and $T-v$ diagrams. (a) At $p=3$ bar, $T=240^{\circ} \mathrm{C}$, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$. (b) At $p=3$ bar, $v=0.5 \mathrm{~m}^{3} / \mathrm{kg}$, find $T$ in ${ }^{\circ} \mathrm{C}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$. (c) At $T=400^{\circ} \mathrm{C}, p=10$ bar, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $h$ in $\mathrm{kJ} / \mathrm{kg}$. (d) At $T=320^{\circ} \mathrm{C}, v=0.03 \mathrm{~m}^{3} / \mathrm{kg}$, find $p$ in $\mathrm{MPa}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$ (e) At $p=28 \mathrm{MPa}, T=520^{\circ} \mathrm{C}$, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $h$ in $\mathrm{kJ} / \mathrm{kg}$. (f) At $T=100^{\circ} \mathrm{C}, x=60 \%$, find $p$ in bar and $v$ in $\mathrm{m}^{3} / \mathrm{kg}$. (g) At $T=10^{\circ} \mathrm{C}, v=100 \mathrm{~m}^{3} / \mathrm{kg}$, find $p$ in $\mathrm{kPa}$ and $h$ in $\mathrm{kJ} / \mathrm{kg}$. (h) At $p=4 \mathrm{MPa}, T=160^{\circ} \mathrm{C}$, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$.

Using the tables for water, determine the specified property data at the indicated states. Check the results using $I T$. In each case, locate the state by hand on sketches of the $p-v$ and $T-v$ diagrams.
(a) At $p=3$ bar, $T=240^{\circ} \mathrm{C}$, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$.
(b) At $p=3$ bar, $v=0.5 \mathrm{~m}^{3} / \mathrm{kg}$, find $T$ in ${ }^{\circ} \mathrm{C}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$.
(c) At $T=400^{\circ} \mathrm{C}, p=10$ bar, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $h$ in $\mathrm{kJ} / \mathrm{kg}$.
(d) At $T=320^{\circ} \mathrm{C}, v=0.03 \mathrm{~m}^{3} / \mathrm{kg}$, find $p$ in $\mathrm{MPa}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$
(e) At $p=28 \mathrm{MPa}, T=520^{\circ} \mathrm{C}$, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $h$ in $\mathrm{kJ} / \mathrm{kg}$.
(f) At $T=100^{\circ} \mathrm{C}, x=60 \%$, find $p$ in bar and $v$ in $\mathrm{m}^{3} / \mathrm{kg}$.
(g) At $T=10^{\circ} \mathrm{C}, v=100 \mathrm{~m}^{3} / \mathrm{kg}$, find $p$ in $\mathrm{kPa}$ and $h$ in $\mathrm{kJ} / \mathrm{kg}$.
(h) At $p=4 \mathrm{MPa}, T=160^{\circ} \mathrm{C}$, find $v$ in $\mathrm{m}^{3} / \mathrm{kg}$ and $u$ in $\mathrm{kJ} / \mathrm{kg}$.

Key Concepts

Water Property Tables

Water property tables are comprehensive compilations of thermodynamic data for water, including properties such as pressure, temperature, specific volume, internal energy, and enthalpy. These tables are divided into regions that correspond to saturated conditions (at the boiling point) and superheated states, and they serve as essential tools for engineers and scientists for analyzing processes involving water as a working fluid.

Phase Diagrams

Phase diagrams, such as the pressure–specific volume (p-v) and temperature–specific volume (T-v) diagrams, are graphical representations that show the state boundaries between different phases (liquid, vapor, and mixtures) of water. These diagrams help locate the state of the system, indicating whether the water is in a compressed liquid, saturated mixture, or superheated vapor state and are fundamental for visualizing thermodynamic behavior during various processes.

Saturated and Superheated States

The classification of water into saturated and superheated states is critical in thermodynamics. Saturated states refer to conditions where liquid and vapor phases coexist in equilibrium, with defined saturation properties like saturated liquid and saturated vapor lines. Superheated states, on the other hand, occur when the water vapor is heated beyond the saturation temperature at a given pressure, significantly altering its properties. Understanding these states is crucial for accurate property determination using the tables.

Quality (x) in Two-phase Mixtures

In two-phase (mixture) regions, the quality (x) represents the mass fraction of vapor present in the liquid-vapor mixture. It is important for calculating the overall properties of the mixture, such as specific volume, internal energy, and enthalpy, by leveraging the known properties of the saturated liquid and saturated vapor states. The concept of quality is vital when dealing with systems undergoing phase change.

Interpolation in Thermodynamic Tables

Interpolation is a mathematical technique used to estimate thermodynamic properties that fall between the discrete values listed in water property tables. Since the exact state conditions of a process might not always match the tabulated data, engineers use interpolation to obtain more accurate property values. This approach is essential when determining properties such as specific volume, temperature, pressure, internal energy, or enthalpy at non-tabulated conditions.

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