Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are temperature T1?
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Ch 18: A Macroscopic Description of Matter
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 18, Problem 35c
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. How many moles of gas are there?
Verified step by step guidance1
Step 1: Identify the relevant equation for the problem. To find the number of moles of gas, we use the Ideal Gas Law: , where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
Step 2: Convert the given temperature from Celsius to Kelvin. The temperature in Kelvin is calculated using the formula: . For 900°C, this becomes .
Step 3: Extract the values of pressure (P) and volume (V) from the graph. At point 2, the pressure is 4 atm and the volume is 8 L. These values will be used in the Ideal Gas Law.
Step 4: Use the gas constant R in appropriate units. For pressure in atm and volume in liters, the value of R is .
Step 5: Rearrange the Ideal Gas Law to solve for n (number of moles): . Substitute the values for P, V, R, and T into the equation to calculate the number of moles.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas. It is expressed as PV = nRT, where R is the ideal gas constant. This law allows us to calculate the number of moles of gas when the other variables are known, making it essential for solving problems involving gas behavior.
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Ideal Gases and the Ideal Gas Law
Pressure-Volume Relationship
The pressure-volume relationship of a gas is described by Boyle's Law, which states that at constant temperature, the pressure of a gas is inversely proportional to its volume. This means that if the volume increases, the pressure decreases, and vice versa. Understanding this relationship is crucial for analyzing the graph provided, which illustrates how pressure changes with volume during the gas's transformation.
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Thermodynamic Processes
Thermodynamic processes describe the changes in state variables of a system, such as temperature, pressure, and volume. In the context of the question, the graph represents a specific process that the gas undergoes, which can be isothermal, adiabatic, or other types. Identifying the type of process is important for applying the correct equations and understanding how the gas behaves under different conditions.
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Related Practice
Textbook Question
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. Show the process on a pV diagram. Include a proper scale on both axes.
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Textbook Question
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. What is the final pressure of the gas?
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Textbook Question
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. What type of process is this?
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Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What is the volume V3?
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Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are pressure p2?
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