Question

Water vapor at \(1000 \mathrm{kPa}\) and \(600^{\circ} \mathrm{C}\) is expanded to 500 kPa and \(400^{\circ} \mathrm{C}\). Calculate the change in the specific entropy and enthalpy of this water vapor using the departure charts and the property tables.

Short answer

Answer: To find the change in specific entropy and specific enthalpy for water vapor, follow these steps: 1. Consult the steam tables to find the initial specific enthalpy (h₁) and specific entropy (s₁) at 1000 kPa and 600°C. 2. Find the final specific enthalpy (h₂) and specific entropy (s₂) at 500 kPa and 400°C from the steam tables. 3. Consult the departure charts to find the ideal specific enthalpy and entropy values and find the difference in departure values for each property. 4. Calculate the change in specific enthalpy: (h₂ - h₁) = (h₂,ideal - h₁,ideal) + (h₂,departure - h₁,departure). 5. Calculate the change in specific entropy: (s₂ - s₁) = (s₂,ideal - s₁,ideal) + (s₂,departure - s₁,departure). 6. Report the changes in specific enthalpy and specific entropy with appropriate units (J/mol-K for specific entropy and J/mol for specific enthalpy).

Step-by-step solution

Find initial specific enthalpy and entropy from property tables

Consult the steam tables (such as the NIST Chemistry WebBook or the Reference Fluid Thermodynamic and Transport Properties Database) for the specific enthalpy \(h_1\) and specific entropy \(s_1\) for water vapor at the initial conditions of \(1000\mathrm{kPa}\) and \(600^{\circ} \mathrm{C}\).

Find final specific enthalpy and entropy from property tables

Retrieve the specific enthalpy \(h_2\) and specific entropy \(s_2\) values for water vapor from the steam tables at the final conditions of \(500\mathrm{kPa}\) and \(400^{\circ} \mathrm{C}\).

Use departure charts

Consult the departure charts (present in some steam tables) for water vapor at the initial and final conditions. Departure charts are used to correct the differences between the values predicted by the ideal gas formula and the actual values observed for a particular substance. These charts provide the ideal specific enthalpy (\(h_{1,ideal}\) and \(h_{2,ideal}\)) and ideal specific entropy (\(s_{1,ideal}\) and \(s_{2,ideal}\)) at corresponding conditions.

Find the difference in specific enthalpy

To find the change in specific enthalpy, calculate the difference between the final and initial experimental values, adjusted for the departure from ideal behavior: \((h_2 - h_1) = (h_{2,ideal} - h_{1,ideal}) + (h_{2,departure} - h_{1,departure})\). It's important to note that departure charts specifically note departure values \((h_{2,departure} - h_{1,departure})\), no need to calculate individual departure values.

Find the difference in specific entropy

The change in specific entropy is obtained in a similar way, using the difference between the final and initial experimental values, and accounting for the difference in departure values for entropy: \((s_2 - s_1) = (s_{2,ideal} - s_{1,ideal}) + (s_{2,departure} - s_{1,departure})\).

Report the results

After computing the changes in specific enthalpy and entropy, report the results with appropriate units (usually in J/mol-K for specific entropy and J/mol for specific enthalpy).

Key concepts

Specific Entropy

Specific entropy, denoted as s, is a measure of the randomness or disorder in a system. In the context of thermodynamics, particularly when studying water vapor like in our exercise, it refers to the entropy per unit mass. It's a state property, meaning it depends only on the current state of the substance, not how it got there.

Understanding specific entropy is crucial when analyzing thermodynamic processes, such as the expansion of water vapor. Changes in specific entropy can indicate the direction of heat transfer, as well as the efficiency of the process. To calculate the change in specific entropy during an expansion, we need to look up the initial and final values of specific entropy from the steam tables corresponding to the given pressures and temperatures, then subtract the initial value from the final value as done in the exercise.

Specific Enthalpy

Specific enthalpy, represented as h, is the total heat content per unit mass of a system. It combines the internal energy of a system with the product of its pressure and volume, effectively quantifying the energy needed to create the system and make room for it by displacing its environment.

In practical terms, specific enthalpy is important for understanding the energy changes during phase transitions or temperature changes of water vapor. In our exercise, the specific enthalpy values are obtained from the steam tables for both initial and final states of the water vapor. The change in specific enthalpy is then the difference between these two values, which represents the heat added or removed during the process.

Steam Tables

Steam tables are an essential tool for any engineer or scientist working with thermodynamic processes. They contain thermophysical properties of water and steam, such as temperature, pressure, specific volume, specific enthalpy, and specific entropy for various states, ranging from liquid to vapor.

By consulting steam tables, you can find precise property data needed for calculating work and heat in thermodynamic cycles. In our problem, the steam tables provide the necessary initial and final values of specific enthalpy and entropy needed for our calculations. These tables save one from tedious and time-consuming calculations using the fundamental thermodynamic equations.

Departure Charts

Departure charts are a visual representation used to account for the difference between real gas behavior and the ideal gas assumption. Real substances, such as water vapor, often deviate from ideal gas behavior, and these deviations become more pronounced at high pressures and temperatures.

These charts offer departure functions for specific enthalpy and entropy, which need to be added or subtracted from the corresponding ideal gas values to obtain accurate results, as outlined in our exercise. By using departure charts along with steam tables, a more precise analysis of thermodynamic processes is achievable, crucial for engineering applications involving steam and power cycles.