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Chapter 2: Problem 69

Is it reasonable to assume that at the given states the substance behaves as an ideal gas? a. Oxygen at \(30^{\circ} \mathrm{C}, 3 \mathrm{MPa}\) b. Methane at \(30^{\circ} \mathrm{C}, 3 \mathrm{MPa}\) c. Water at \(30^{\circ} \mathrm{C}, 3 \mathrm{MPa}\) d. \(\mathrm{R}-134 \mathrm{a}\) at \(30^{\circ} \mathrm{C}, 3 \mathrm{MPa}\) e. \(\mathrm{R}-134 \mathrm{a}\) at \(30^{\circ} \mathrm{C}, 100 \mathrm{kPa}\)

Short Answer

Expert verified
Oxygen and methane likely behave as ideal gases, water does not, and R-134a can be considered ideal at both pressures.

Step by step solution

01

Understand Ideal Gas Assumptions

Identify the criteria for a substance to behave as an ideal gas. Generally, gases behave more ideally at high temperatures and low pressures compared to their critical temperature and critical pressure.
02

Analyze Critical Points

For each substance, compare the given conditions to its critical temperature and critical pressure. Critical points are specific properties of substances at which they no longer behave as a typical gas before continuing to a supercritical fluid.
03

Evaluate Oxygen at Given Conditions

Oxygen has a critical temperature of about 154.6 K and a critical pressure of around 5.043 MPa. At 30掳C (303.15 K) and 3 MPa, the temperature is well above critical but the pressure is below. Oxygen is likely to behave nearly as an ideal gas.
04

Evaluate Methane at Given Conditions

Methane has a critical temperature of around 190.6 K and a critical pressure of approximately 4.6 MPa. At 30掳C (303.15 K) and 3 MPa, the temperature is above critical but the pressure falls below its critical value, allowing methane to approximate ideal gas behavior.
05

Evaluate Water at Given Conditions

Water has a critical temperature of 647.1 K and a critical pressure of 22.064 MPa. At 30掳C and 3 MPa, water is far below its critical temperature, which means it's not likely to behave as an ideal gas.
06

Evaluate R-134a at Given Conditions (3 MPa)

R-134a has a critical temperature of 374.2 K and a critical pressure of 4.059 MPa. The conditions of 30掳C and 3 MPa are both below critical levels; hence, R-134a can approximate ideal gas behavior.
07

Evaluate R-134a at Lower Pressure (100 kPa)

At 30掳C (well below the critical temperature) and 100 kPa (significantly lower than the critical pressure), R-134a is under conditions where it can be considered to behave as an ideal gas.

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Key Concepts

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

Critical Temperature
The critical temperature of a substance is a key concept in understanding ideal gas behavior. It refers to the highest temperature at which a gas can be converted into a liquid, regardless of how much pressure is applied. Beyond this point, the substance does not behave as a typical liquid or gas, entering a supercritical state instead.
  • For each substance, if the given temperature is higher than its critical temperature, it is more likely to act like an ideal gas.
  • At temperatures below the critical temperature, the substance may exhibit liquid-like properties, deviating from ideal gas behavior.
Knowing the critical temperature helps in predicting the thermodynamic behavior of gases under different conditions, making it crucial for evaluating how substances might behave as gases or liquids in a mixture.
Critical Pressure
Critical pressure is the minimum pressure required to liquefy a gas at its critical temperature. This concept helps us understand the pressure limits for ideal gas behavior. When pressure is lower than a substance's critical pressure, it is more likely to behave as an ideal gas, especially if the temperature is high.
  • If the pressure exceeds the critical pressure, especially at or near the critical temperature, the gas might become a liquid or a supercritical fluid, showing non-ideal behavior.
  • Evaluating a substance's pressure in relation to its critical pressure is key to determining how it will behave as an ideal gas.
By assessing the critical pressure, we can predict under which conditions a gas phase might closely follow the ideal gas laws.
Gas Laws
Gas laws, such as Boyle's law, Charles's law, and the Ideal Gas Law, describe how gases behave in relation to pressure, volume, and temperature. The Ideal Gas Law combines these relationships and is represented as \(PV = nRT\), where:
  • \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is temperature.
Gas laws assume that gas molecules are in constant motion and have elastic collisions, with no volume and no intermolecular attractions.
  • These assumptions hold true for gases at high temperatures and low pressures compared to their critical points.
  • Gas laws help predict how a substance will behave under different pressures and temperatures.
Understanding gas laws is fundamental for assessing when and how a gas behaves ideally.
Thermodynamic Properties
Thermodynamic properties help describe the behavior of substances across different states, including gases, liquids, and solids. They include properties such as pressure, temperature, volume, and internal energy.
  • These properties are useful in predicting how gases will behave when subjected to changes in environmental conditions.
  • Critical temperature and pressure are particular thermodynamic properties that determine the boundary between liquid and gas phases.
By analyzing thermodynamic properties, we can determine deviations from ideal gas behavior, especially near critical points or when external conditions shift significantly. This understanding is essential for practical applications, like calculating engine efficiency or predicting weather phenomena. Knowing these properties helps in designing processes and systems that incorporate gases.

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Most popular questions from this chapter

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