/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 If you put a helium-filled ballo... [FREE SOLUTION] | 91Ó°ÊÓ

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If you put a helium-filled balloon in the refrigerator, (a) will its volume increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. Lowering the temperature of an ideal gas at constant pressure results in a reduced volume. II. The same amount of gas is in the balloon; therefore, its volume remains the same. III. The balloon can expand more in the cool air of the refrigerator, giving an increased volume.

Short Answer

Expert verified
(a) The volume decreases. (b) Explanation I is correct.

Step by step solution

01

Understand the Problem

We need to determine what happens to the volume of a helium-filled balloon when placed in the refrigerator. We are given three statements to choose from as explanations for the observed behavior.
02

Recall Gas Law Principles

According to Charles's Law, for an ideal gas at constant pressure, the volume is directly proportional to its temperature in Kelvin: \( V \propto T \). Thus, reducing the temperature leads to a decrease in volume if the pressure is constant.
03

Evaluate Statement I

Statement I says lowering the temperature at constant pressure results in reduced volume. This aligns with Charles's Law, which states that if the temperature decreases, the volume also decreases when pressure is constant. Hence, this statement is correct.
04

Evaluate Statement II

Statement II mentions that the volume remains the same because the same amount of gas is present. Earlier, we established that volume changes with temperature when pressure is constant. Thus, this statement is incorrect because it doesn't consider the temperature effect.
05

Evaluate Statement III

Statement III suggests the balloon will expand in the cool air, leading to an increased volume. This contradicts the principles of Charles’s Law because decreasing temperature at constant pressure decreases volume. Therefore, this statement is incorrect.
06

Conclusion and Selection

Lowering the temperature decreases the volume according to Charles's Law, making statement I the best explanation. Hence, the volume of the balloon will decrease. Statement I is the correct explanation.

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Key Concepts

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

Ideal Gas Behavior
In the realm of gases, we often refer to the concept of ideal gas behavior. This is a simplified model of how gases are expected to act under various conditions. Although most gases do not behave perfectly as ideal gases, this model provides us with a useful approximation. When a gas behaves ideally, its particles are assumed to have no interaction with each other, and occupy no space themselves.
The behavior of an ideal gas is governed by the Ideal Gas Law, which is formulated as \( PV = nRT \). In this equation, \(P\) represents pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
This law highlights how these variables interact. For an ideal gas, changes in temperature, volume, and pressure can be predicted reliably. Understanding these behaviors helps clarify how gases like the helium in our balloon react under various conditions.
Volume-Temperature Relationship
Charles's Law is central to understanding the volume-temperature relationship of gases. This law states that at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin. Simply put, if you increase the temperature of a gas, its volume increases, and if you decrease the temperature, its volume decreases.
Mathematically, this is expressed as \( V \propto T \), meaning \( V/T = \text{const.} \). So, if a helium balloon is placed in a refrigerator, the temperature drops, thereby decreasing its volume.
This law makes it evident that gases are highly responsive to temperature changes. Always remember, the relationship holds only when pressure remains unchanged—otherwise, other factors must be considered.
Constant Pressure Effects
When discussing the constant pressure effects on a gas, it's crucial to consider the constraints that come with it. For our balloon scenario, constant pressure means the pressure inside the balloon does not change, even as temperature varies.
By maintaining constant pressure, and reducing the temperature, the volume must decrease according to Charles's Law. This is because, as the gas inside cools, its kinetic energy reduces, the molecules move slower, and their ability to push against the balloon's walls diminishes.
Let’s outline why understanding these pressure effects is essential:
  • It helps predict how gas volumes change in real-world situations.
  • Knowing these effects assists in designing systems where gas volumes must be controlled.
Hence, under constant pressure, observing the volume changes becomes straightforward by applying Charles's Law.

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