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Chapter 4: Problem 72

A large pipe carries steam as a two-phase liquid-vapor mixture at \(1.0 \mathrm{MPa}\). A small quantity is withdrawn through a throttling calorimeter, where it undergoes a throttling process to an exit pressure of \(0.1 \mathrm{MPa}\). For what range of exit temperatures, in \({ }^{\circ} \mathrm{C}\), can the calorimeter be used to determine the quality of the steam in the pipe? What is the corresponding range of steam quality values?

Short Answer

Expert verified
Exit temperatures: \textgreater 45.8掳C. Corresponding steam quality range: determined by enthalpy values at pressures 1.0 MPa and 0.1 MPa.

Step by step solution

01

- Understanding the Problem

The goal is to find the range of exit temperatures and corresponding steam quality values for a throttling calorimeter process. Given data: initial pressure of 1.0 MPa and exit pressure of 0.1 MPa.
02

- Determine Saturation Temperatures

Look up the saturation temperatures for water at the given pressures using steam tables. The saturation temperature at 1.0 MPa is approximately 179.9掳C.
03

- Utilize Throttling Process Properties

In a throttling process, enthalpy remains constant. Therefore, the enthalpy of the steam at 1.0 MPa and the initial quality is equal to the enthalpy at 0.1 MPa.
04

- Saturation Temperature at Exit Pressure

To ensure that a two-phase mixture exists at the exit, check the saturation temperature at 0.1 MPa. It's approximately 45.8掳C.
05

- Quality at Exit Pressure Range

For the calorimeter to be useful, the exit temperature should be between the saturation temperature and superheated temperature at 0.1 MPa. Use steam tables to determine the range.
06

- Corresponding Range of Steam Quality Values

Calculate the quality of steam in the pipe by finding the enthalpy at 1.0 MPa for the given temperatures and pressures using interpolation if necessary.
07

- Final Range Calculation

For the saturation range, the exit temperature should be 45.8掳C or higher. Quality values can then be determined from the enthalpy balance at both ends of the range.

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Key Concepts

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

Steam Quality
Steam quality, often represented as 'x,' is a measure of the proportion of steam in a liquid-vapor mixture. It's a value between 0 (all liquid) to 1 (all vapor). In practical applications, knowing the steam quality is important for understanding the energy content and efficiency of steam in processes.
For instance, in a throttling calorimeter, steam quality is determined by analyzing the changes in pressure and temperature during the throttling process.
A higher steam quality indicates a higher proportion of vapor in the mixture, which translates to higher energy content per unit mass. Measuring steam quality helps in various engineering and industrial processes where steam's thermal properties are crucial.
Saturation Temperature
Saturation temperature is the temperature at which a liquid boils and turns into vapor at a given pressure. In the context of steam tables, it鈥檚 crucial because it defines the temperature at which liquid water turns into steam at a specific pressure.
For example, at 1.0 MPa, the saturation temperature is approximately 179.9掳C, meaning water will boil and turn into steam at this temperature under this pressure. Understanding saturation temperature is essential when working with steam because processes often depend on precise temperature and pressure conditions.
In a throttling calorimeter, it's important to ensure the steam is in both phases by cross-referencing the saturation temperatures at the initial and exit pressures.
Enthalpy
Enthalpy, represented as 'h,' is a measure of the total energy content in a thermodynamic system, per unit mass. It includes both internal energy and the energy required to make room for the substance (pressure-volume work). Enthalpy is crucial in processes involving heat exchange and phase changes.
In a throttling process, the enthalpy remains constant. This property helps in determining the steam quality by comparing the initial and final states of the steam.
For instance, if steam at 1.0 MPa undergoes throttling to 0.1 MPa, the enthalpy before and after the throttling process remains the same. This constant enthalpy can be used to find the quality of the steam at the exit pressure by using steam tables and known saturation temperatures.
Thus, understanding how to calculate and utilize enthalpy is vital in analyzing and designing systems that involve thermal energy transformations.

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Most popular questions from this chapter

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