Skip to main content
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 64a
Chapter 18, Problem 64a

10 g of dry ice (solid CO₂) is placed in a 10,000 cm3 container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which CO₂ is a gas. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm3.

Verified step by step guidance
1
Step 1: Calculate the number of moles of CO₂. Use the formula for moles: \( n = \frac{m}{M} \), where \( m \) is the mass of CO₂ (10 g) and \( M \) is the molar mass of CO₂ (44 g/mol).
Step 2: Use the ideal gas law to calculate the initial pressure of the gas. The ideal gas law is \( PV = nRT \), where \( P \) is pressure, \( V \) is volume (10,000 cm³ converted to liters), \( n \) is the number of moles, \( R \) is the gas constant (0.0821 L·atm/(mol·K)), and \( T \) is the temperature in Kelvin (0°C = 273 K). Rearrange the equation to solve for \( P \): \( P = \frac{nRT}{V} \).
Step 3: For the isothermal compression, use the relationship \( P_1V_1 = P_2V_2 \) (Boyle's Law). Here, \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure (3.0 atm) and the unknown volume after the isothermal compression. Solve for \( V_2 \): \( V_2 = \frac{P_1V_1}{P_2} \).
Step 4: For the isobaric compression, the pressure remains constant at 3.0 atm. The final volume is given as 1000 cm³ (or 1.0 L). Use the ideal gas law again to calculate the final temperature \( T_f \) after the isobaric compression. Rearrange the ideal gas law to solve for \( T_f \): \( T_f = \frac{P_fV_f}{nR} \), where \( P_f \) is the final pressure, \( V_f \) is the final volume, \( n \) is the number of moles, and \( R \) is the gas constant.
Step 5: Summarize the process. First, calculate the initial pressure using the ideal gas law. Then, determine the intermediate volume after the isothermal compression using Boyle's Law. Finally, calculate the final temperature after the isobaric compression using the ideal gas law. Ensure all units are consistent throughout the calculations.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
6m
Was this helpful?

Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it helps determine the pressure of CO₂ gas in the container at 0°C, where n is the number of moles of CO₂, R is the ideal gas constant, and T is the absolute temperature in Kelvin.
Recommended video:
Guided course
07:21
Ideal Gases and the Ideal Gas Law

Isothermal Process

An isothermal process occurs when a gas is compressed or expanded at a constant temperature. During this process, the internal energy of the gas remains constant, and any work done on or by the gas results in heat exchange with the surroundings. This concept is crucial for understanding how the gas pressure changes during the isothermal compression phase described in the question.
Recommended video:
Guided course
06:13
Entropy & Ideal Gas Processes

Isobaric Process

An isobaric process is one in which the pressure remains constant while the volume and temperature of the gas change. In this scenario, the gas undergoes an isobaric compression, meaning that as the volume decreases to 1000 cm³, the pressure will remain at 3.0 atm, allowing for calculations of temperature changes and the behavior of the gas under these conditions.
Recommended video:
Guided course
06:44
Heat Equations for Isobaric & Isovolumetric Processes
Related Practice
Textbook Question

A diver 50 m deep in 10°C fresh water exhales a 1.0-cm-diameter bubble. What is the bubble's diameter just as it reaches the surface of the lake, where the water temperature is 20°C?

1
views
Textbook Question

The 50 kg circular piston shown in FIGURE P18.57 floats on 0.12 mol of compressed air. How far does the piston move if the temperature is increased by 100°C?

2
views
Textbook Question

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. What is the gas temperature after the expansion (in °C)? The gas pressure is then decreased at constant volume until the original temperature is reached.

1
views
Textbook Question

In Problems 67,68,69,67, 68, 69, and 7070 you are given the equation(s) used to solve a problem. For each of these, you are to draw a pV diagram.

(T2+273) K=200 kPa500 kPa×1×(400+273) K(T_2 + 273) \(\text{ K}\) = \(\frac{200 \text{ kPa}\)}{500 \(\text{ kPa}\)} \(\times\) 1 \(\times\) (400 + 273) \(\text{ K}\)

1
views
Textbook Question

A container of gas at 2.0 atm pressure and 127°C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again. Show this process on a pV diagram.

2
views
Textbook Question

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. What is the gas volume after the expansion?

1
views