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Ch 18: A Macroscopic Description of Matter
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 18: A Macroscopic Description of MatterProblem 32b
Chapter 18, Problem 32b

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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Step 1: Understand the problem. The gas undergoes an isochoric process, meaning the volume remains constant. The initial temperature is 20°C (convert to Kelvin: T₁ = 20 + 273 = 293 K), and the final temperature is 300°C (convert to Kelvin: T₂ = 300 + 273 = 573 K). The volume of the container is 50 cm³, which remains constant throughout the process.
Step 2: Use the ideal gas law to determine the pressure at both temperatures. The ideal gas law is given by: P = (nRT)/V, where n is the number of moles, R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and V is the volume in cubic meters. Convert the volume from cm³ to m³: V = 50 cm³ × (1 m³ / 10⁶ cm³) = 50 × 10⁻⁶ m³.
Step 3: Calculate the initial pressure (P₁) using the ideal gas law. Substitute the values: n = 0.10 mol, R = 8.314 J/(mol·K), T₁ = 293 K, and V = 50 × 10⁻⁶ m³. This gives P₁ = (0.10 × 8.314 × 293) / (50 × 10⁻⁶).
Step 4: Calculate the final pressure (P₂) using the ideal gas law. Substitute the values: n = 0.10 mol, R = 8.314 J/(mol·K), T₂ = 573 K, and V = 50 × 10⁻⁶ m³. This gives P₂ = (0.10 × 8.314 × 573) / (50 × 10⁻⁶).
Step 5: Plot the process on a pV diagram. Since the volume remains constant, the graph will be a vertical line at V = 50 cm³ (or 50 × 10⁻⁶ m³). The pressure axis should be scaled to include both P₁ and P₂, and the volume axis should remain fixed at 50 cm³. Label the initial and final pressures on the graph accordingly.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isochoric Process

An isochoric process is a thermodynamic process in which the volume of the system remains constant. In this scenario, the argon gas is heated in a fixed-volume container, meaning that any increase in temperature will result in an increase in pressure, as the gas molecules gain kinetic energy and collide more frequently with the walls of the container.
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Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas, where n is the number of moles and R is the ideal gas constant. This law is crucial for understanding the behavior of the argon gas in the container, as it allows us to calculate changes in pressure resulting from the increase in temperature during the isochoric heating.
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pV Diagram

A pV diagram is a graphical representation of the relationship between pressure (p) and volume (V) for a given system. In this case, the pV diagram will illustrate the isochoric process of the argon gas, showing a vertical line since the volume remains constant while the pressure increases as the temperature rises from 20°C to 300°C.
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Related Practice
Textbook Question

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A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. How many moles of gas are there?

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A gas with initial state variables p1, V1, and T1 expands isothermally until V2 = 2V1. What are p2?

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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

A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303°C. The air above the piston is at 1.00 atm pressure. What will the height of the piston be if the temperature is lowered to 15°C?

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