Chapter 11: Problem 62
What volume is occupied by an ideal gas at absolute zero?
Short Answer
Expert verified
At absolute zero, the volume of an ideal gas is zero.
Step by step solution
01
Understanding Absolute Zero
Absolute zero is theoretically the lowest temperature possible, and it is 0 Kelvin (-273.15°C). According to the ideal gas law, at this temperature, the motion of gas molecules ceases entirely.
02
Reviewing the Ideal Gas Law
The ideal gas law is given by the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature in Kelvin.
03
Substituting for Absolute Zero
When we substitute \( T = 0 \) K into the ideal gas law equation, \( PV = nR(0) \) becomes \( PV = 0 \). It implies that the product \( PV \) is zero when temperature is absolute zero.
04
Analyzing the Equation
Given \( PV = 0 \), either \( P \), \( V \), or both must also be zero. Physically, this means that at absolute zero, the volume must be zero, because, for a gas to have zero volume theoretically means it doesn't exist in physical space.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Absolute Zero
The concept of absolute zero is fundamental to understanding temperature scales and thermodynamics. Absolute zero is the point at which the kinetic energy of gas molecules theoretically ceases. This means all molecular motion stops. This occurs at 0 Kelvin, which is equivalent to -273.15°C or -459.67°F.
At this extreme temperature, an ideal gas would theoretically occupy no volume. This is because the lack of molecular motion implies no pressure exertion, resulting in zero volume according to the ideal gas law. In practice, researchers can get very close to absolute zero, but achieving it is impossible. Absolute zero is more of a limit rather than an attainable temperature.
Understanding absolute zero is crucial for studying physical phenomena related to low-temperature environments. It helps scientists and engineers to design experiments and technology that operate efficiently at extremely low temperatures.
At this extreme temperature, an ideal gas would theoretically occupy no volume. This is because the lack of molecular motion implies no pressure exertion, resulting in zero volume according to the ideal gas law. In practice, researchers can get very close to absolute zero, but achieving it is impossible. Absolute zero is more of a limit rather than an attainable temperature.
Understanding absolute zero is crucial for studying physical phenomena related to low-temperature environments. It helps scientists and engineers to design experiments and technology that operate efficiently at extremely low temperatures.
Temperature
Temperature is a measure of the average kinetic energy of particles in a substance. In the context of gases, temperature is crucial because it affects how gas molecules move and interact.
Higher temperatures mean greater molecular motion, leading to increased pressure and volume if the gas is free to expand. Conversely, lower temperatures reduce this motion. In theoretical contexts like absolute zero, temperature plays a critical role in the volume of an ideal gas.
Both the Celsius and Kelvin scales are used to measure temperature, but Kelvin is particularly useful in scientific calculations. This is because it starts at absolute zero, where the theoretical volume of an ideal gas is zero. Without an understanding of temperature's role, much of thermodynamics and the behavior of gases would remain a mystery.
Higher temperatures mean greater molecular motion, leading to increased pressure and volume if the gas is free to expand. Conversely, lower temperatures reduce this motion. In theoretical contexts like absolute zero, temperature plays a critical role in the volume of an ideal gas.
Both the Celsius and Kelvin scales are used to measure temperature, but Kelvin is particularly useful in scientific calculations. This is because it starts at absolute zero, where the theoretical volume of an ideal gas is zero. Without an understanding of temperature's role, much of thermodynamics and the behavior of gases would remain a mystery.
Volume
Volume is the space that a gas occupies. According to the ideal gas law, volume is directly related to the number of moles of gas and temperature, inversely related to pressure.
Understanding volume in the context of gases requires grasping how changes in pressure and temperature can cause a gas to expand or contract. If temperature drops to absolute zero, theoretically, the volume of an ideal gas becomes zero.
In essence, volume reflects the conditions under which a gas exists. Without pressure or temperature to contain it, a gas could expand infinitely, but with boundaries such as a container, its volume can be measured and predicted using the ideal gas law.
Kelvin
The Kelvin scale is indispensable in scientific disciplines, especially when dealing with gases. Unlike Celsius or Fahrenheit, Kelvin is an absolute scale that starts at absolute zero, the theoretical point where an ideal gas would have zero volume and molecular movement would cease.
Using Kelvin in calculations, particularly with the ideal gas law, eliminates negative temperature values, which simplifies equations. This makes it highly useful for scientists and engineers who need to predict behaviors at extreme temperatures.
In the Kelvin scale, each degree is equal in magnitude to those on the Celsius scale, making it easier for international scientific collaboration. The importance of Kelvin lies not just in its practicality but also in its alignment with physical principles, providing a true measure of thermal energy devoid of arbitrary baselines found in other scales.
Using Kelvin in calculations, particularly with the ideal gas law, eliminates negative temperature values, which simplifies equations. This makes it highly useful for scientists and engineers who need to predict behaviors at extreme temperatures.
In the Kelvin scale, each degree is equal in magnitude to those on the Celsius scale, making it easier for international scientific collaboration. The importance of Kelvin lies not just in its practicality but also in its alignment with physical principles, providing a true measure of thermal energy devoid of arbitrary baselines found in other scales.
