**Thermodynamics: Calculating Work Done by an Expanding Gas****Problem Statement:**Consider an ideal gas enclosed in a 1.00 L container at an internal pressure of 24.0 atm. Calculate the work, \( w \), if the gas expands against a constant external pressure of 1.00 atm to a final volume of 24.0 L.**Single-Step Expansion:**- Formula for work done by gas: \[ w = -P_{\text{ext}} \Delta V \]- Initial Calculation: \( w = -810.64 \) J- Note: The calculated value is marked as incorrect.**Two-Step Expansion Process:**1. **First Step:** - Let the gas expand against a constant external pressure of 1.50 atm to a volume of 16.0 L.2. **Second Step:** - From the endpoint of step 1, let the gas expand to 24.0 L against a constant external pressure of 1.00 atm.- Final Calculation for Two-Step Process: \( w = 3090.565 \) J- Note: This calculated value is also marked as incorrect.**Summary:**This exercise involves calculating the work done by an ideal gas when expanding. The setup involves both a single-step and a two-step expansion process to illustrate different methods of calculation; however, both attempts resulted in incorrect calculations. Further analysis and calculation adjustments are needed for accurate results.

Given that : The internal pressure of the gas = 24.0 atm The initial volume of the container = 1.00…

Consider an ideal gas enclosed in a 1.00 L container at an internal pressure of 24.0 atm. Calculate the work, w, if the gas expands against a constant external pressure of 1.00 atm to a final volume of 24.0 L. -810.64 w = J Incorrect Now calculate the work done if this process is carried out in two steps. 1. First, let the gas expand against a constant external pressure of 1.50 atm to a volume of 16.0 L. 2. From the end point of step 1, let the gas expand to 24.0 L against a constant external pressure of 1.00 atm. 3090.565 w = J Incorrect

Consider an ideal gas enclosed in a 1.00 L container at an internal pressure of 24.0 atm. Calculate the work, w, if the gas expands against a constant external pressure of 1.00 atm to a final volume of 24.0 L. -810.64 w = J Incorrect Now calculate the work done if this process is carried out in two steps. 1. First, let the gas expand against a constant external pressure of 1.50 atm to a volume of 16.0 L. 2. From the end point of step 1, let the gas expand to 24.0 L against a constant external pressure of 1.00 atm. 3090.565 w = J Incorrect

Chemistry: Principles and Practice

3rd Edition

ISBN:9780534420123

Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Chapter17: Chemcial Thermodynamics

Section: Chapter Questions

Problem 17.33QE: A 220-L cylinder contains an ideal gas at a pressure of 150 atm. If the gas is allowed to expand...

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Question

**Thermodynamics: Calculating Work Done by an Expanding Gas**

**Problem Statement:**

Consider an ideal gas enclosed in a 1.00 L container at an internal pressure of 24.0 atm. Calculate the work, \( w \), if the gas expands against a constant external pressure of 1.00 atm to a final volume of 24.0 L.

**Single-Step Expansion:**

- Formula for work done by gas:

\[ w = -P_{\text{ext}} \Delta V \]

- Initial Calculation:

\( w = -810.64 \) J

- Note: The calculated value is marked as incorrect.

**Two-Step Expansion Process:**

1. **First Step:**
- Let the gas expand against a constant external pressure of 1.50 atm to a volume of 16.0 L.

2. **Second Step:**
- From the endpoint of step 1, let the gas expand to 24.0 L against a constant external pressure of 1.00 atm.

- Final Calculation for Two-Step Process:

\( w = 3090.565 \) J

- Note: This calculated value is also marked as incorrect.

**Summary:**

This exercise involves calculating the work done by an ideal gas when expanding. The setup involves both a single-step and a two-step expansion process to illustrate different methods of calculation; however, both attempts resulted in incorrect calculations. Further analysis and calculation adjustments are needed for accurate results.

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