Textbook Question
A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare the average kinetic energies of the three types of atoms.
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Ch 18: Thermal Properties of Matter
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 18, Problem 25
In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about people)?
Verified step by step guidance1
First, understand that the problem involves calculating the volume of a cube that contains a specific number of molecules, equivalent to the population of the Earth, which is approximately 7 * 10^9 molecules.
Next, recall that at standard conditions (0°C and 1 atm), one mole of an ideal gas occupies 22.4 liters. Use Avogadro's number, which is approximately 6.022 * 10^23 molecules per mole, to find the volume occupied by 7 * 10^9 molecules.
Calculate the number of moles corresponding to 7 * 10^9 molecules using the formula: \( \text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} \).
Determine the volume occupied by these moles using the relation: \( \text{Volume} = \text{Number of moles} \times 22.4 \text{ liters/mole} \).
Finally, find the length of the side of the cube by taking the cube root of the volume in liters, since the volume of a cube is given by \( \text{Volume} = \text{side length}^3 \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Avogadro's Number
Avogadro's Number is a fundamental constant in chemistry and physics, representing the number of constituent particles, usually atoms or molecules, in one mole of a substance. It is approximately 6.022 x 10^23 particles per mole. This concept is crucial for converting between the number of molecules and moles, which is necessary for calculating the volume of gas containing a specific number of molecules.
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Ideal Gas Law
The Ideal Gas Law is a fundamental equation in physics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed 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. This law helps determine the volume occupied by a given number of molecules under standard conditions.
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Standard Conditions
Standard conditions refer to a set of agreed-upon reference conditions for temperature and pressure used in scientific calculations. Typically, these are 0°C (273.15 K) and 1 atm pressure. Understanding standard conditions is essential for applying the Ideal Gas Law to find the volume of a gas, as it provides a baseline for calculations involving gases.
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Related Practice
Textbook Question
Modern vacuum pumps make it easy to attain pressures of the order of atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. At a pressure of atm and an ordinary temperature of K, how many molecules are present in a volume of cm3?
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Textbook Question
What is the total translational kinetic energy of the air in an empty room that has dimensions m m m if the air is treated as an ideal gas at atm?
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Textbook Question
A large organic molecule has a mass of kg. What is the molar mass of this compound?
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Textbook Question
Consider an ideal gas at °C and atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. What is the length of an edge of each cube if adjacent cubes touch but do not overlap?
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Textbook Question
Modern vacuum pumps make it easy to attain pressures of the order of atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. How many molecules would be present at the same temperature but at atm instead?
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