91Ó°ÊÓ

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

Step by step solution

01

Understand the problem

We need to find thermodynamic property data for water at different states using given pressure, specific volume, and temperature values. Each sub-question (a) to (e) requires location on the property diagrams and calculation of specific properties.

02

Use steam tables for calculation

Use the steam tables to locate the values of different properties such as temperature (T), specific internal energy (u), specific enthalpy (h), specific volume (v), and pressure (p) as needed.

03

Sub-question (a)

Given: - Pressure, \( p = 3 \text{ bar (or 300 kPa)} \)- Specific volume, \( v = 0.5 \mathrm{~m^3 / kg} \). From steam tables:- At 300 kPa, the specific volumes for saturated liquid and vapor are determined. Since \( 0.5 \mathrm{~m^3 / kg} \) lies between these values, the state is in superheated region. Using superheated steam table for 300 kPa and specific volume near 0.5 \mathrm{~m^3 / kg}: \( T \approx 250^{\text{°C}} \) \( u \approx 2600 \mathrm{~kJ/kg} \).

04

Sub-question (b)

Given: - Temperature, \( T = 320^{\text{°C}} \)- Specific volume, \( v = 0.03 \mathrm{~m^3 / kg} \). From steam tables:- At 320 \(^\text{°C} \), find corresponding specific volume for superheated vapor.Calculate values from the superheated steam tables:\( p \approx 13 \text{ MPa} \) \( u \approx 2450 \mathrm{~kJ/kg} \).

05

Sub-question (c)

Given: - Pressure, \( p = 28 \text{ MPa} \)- Temperature, \( T = 520^{\text{°C}} \). From superheated steam tables for 28 MPa and 520°C:\( v = 0.0065 \mathrm{~m^3 / kg} \) \( h \approx 3500 \mathrm{~kJ/kg} \).

06

Sub-question (d)

Given: - Temperature, \( T = 10^{\text{°C}} \)- Specific volume, \( v = 100 \mathrm{~m^3 / kg} \). From steam tables:- Check for saturated liquid and gas states near 10°C. Here, the specific volume is extremely high, indicating a very low pressure (near vacuum).\( p \approx 0.1 \text{ kPa} \) \( h \approx 2500 \mathrm{~kJ/kg} \).

07

Sub-question (e)

Given: - Pressure, \( p = 4 \text{ MPa} \)- Temperature, \( T = 160^{\text{°C}} \). Use tables to determine the specific volume \( v \) and specific internal energy \( u \). At 4 MPa and 160°C (in superheated region):\( v = 0.05 \mathrm{~m^3 / kg} \)\( u \approx 2110 \mathrm{~kJ/kg} \).

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Key Concepts

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

steam tables

Steam tables are vital tools in thermodynamics that contain data on various properties of water and steam across different temperatures and pressures. They allow us to find properties such as specific volume, internal energy, and enthalpy. By using these tables, we can easily determine the values needed for calculations involving water and steam in different states.

• **Saturated**: This refers to a state where water can exist in equilibrium between liquid and vapor phases. Tables for saturated water provide values at the boundary between liquid and vapor.
• **Superheated**: Refers to steam that is not in equilibrium and has a temperature higher than the saturation temperature for a given pressure. Superheated steam tables show values specific to this state.

Steam tables differentiate between these phases, helping us find the right property values for specific conditions. This is essential for solving many thermodynamics exercise problems accurately.
Using steam tables effectively takes practice and experience, ensuring we read the correct values and match them to the desired state accurately.

specific volume

Specific volume is an important property in thermodynamics that refers to the volume per unit mass of a substance, typically expressed in \( \text{m}^3/\text{kg} \). It is the reciprocal of density and provides insight into the compactness of a substance under certain conditions.

• **Formula**: \[ v = \frac{V}{m} \] where V is the volume and m is the mass.
• **Role in Thermodynamics**: Specific volume helps in identifying the state of the substance, whether it's liquid, vapor, or a mixture. It is especially crucial in processes involving phase changes or thermal energy exchange.

In practice, knowing specific volume helps locate the corresponding temperature or pressure from steam tables. This guides us to understand whether the water is in saturated, sub-cooled, or superheated states. For example, in problem (a), knowing that the specific volume between certain values indicates the state is superheated allows us to use the right section of steam tables to find the temperature and internal energy.

superheated steam

Superheated steam is steam that has been heated beyond its boiling point for a specific pressure. In this state, it is not in equilibrium with liquid water, meaning it can carry more energy without immediately condensing.

• **Properties**: Superheated steam has higher temperature and lower density than saturated steam for the same pressure. It is often used in turbines and engines due to its increased energy content.
• **Determination**: From steam tables, if the specific volume or temperature exceeds the saturation point for a given pressure, the steam is superheated. This allows for accurate determination of other properties such as enthalpy and internal energy.

Superheated steam tables list properties for steam that is heated beyond these equilibrium states. They are indispensable in engineering applications where steam is used as a working fluid, as they ensure efficiency by providing precise data for conditions beyond simple phase change.