### Work Done by Gas During Expansion#### Problem Statement:A gas expands according to the pressure-volume graph shown in the drawing. How much work \( W \) is done by the gas in going from point A to point B? Be sure to include the correct algebraic sign.#### Graph Analysis:The provided graph is a Pressure-Volume (P-V) diagram, where:- The y-axis represents the Pressure (in \( \times 10^5 \, \text{Pa} \)).- The x-axis represents the Volume (in \( \text{m}^3 \)).The process described involves a gas expanding:- From point A (4.0 \( \times 10^5 \, \text{Pa} \), 0.30 \( \text{m}^3 \))- To point B (2.0 \( \times 10^5 \, \text{Pa} \), 0.75 \( \text{m}^3 \))The graph consists of two linear segments:1. From (4.0 \( \times 10^5 \, \text{Pa} \), 0.30 \( \text{m}^3 \)) to (2.0 \( \times 10^5 \, \text{Pa} \), 0.60 \( \text{m}^3 \))2. From (2.0 \( \times 10^5 \, \text{Pa} \), 0.60 \( \text{m}^3 \)) to (2.0 \( \times 10^5 \, \text{Pa} \), 0.75 \( \text{m}^3 \))#### Calculation:To find the work done \( W \) by the gas, we calculate the area under the P-V curve.1. **First Segment (A to midpoint):** - Pressure \( P \) changes linearly from 4.0 \( \times 10^5 \, \text{Pa} \) to 2.0 \( \times 10^5 \, \text{Pa} \). - Volume \( V \) changes from 0.30 \( \text{m}^3 \) to 0.60 \( \text{m}^3 \). Area of this trapezoid: \[ W_1

Here Initial pressure = P1 = 4.0×105 Pa Final pressure = P2 = P3 = 2.0×105 Pa Initial volume = V1 =…

A gas expands according to the pressure-volume graph shown in the drawing. How much work W is done by the gas in going from A to B? Be sure to include the correct algebraic sign. Pressure ( 10³ Pa) 0.30 B 0.60 0.75 Volume, m²

A gas expands according to the pressure-volume graph shown in the drawing. How much work W is done by the gas in going from A to B? Be sure to include the correct algebraic sign. Pressure ( 10³ Pa) 0.30 B 0.60 0.75 Volume, m²

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Ideal Gas Law

Ideal gas law states that the product of pressure and volume of a gas directly varies with the product of the number of moles, the universal gas constant, and the temperature of the gas.

Question

### Work Done by Gas During Expansion

#### Problem Statement:
A gas expands according to the pressure-volume graph shown in the drawing. How much work \( W \) is done by the gas in going from point A to point B? Be sure to include the correct algebraic sign.

#### Graph Analysis:
The provided graph is a Pressure-Volume (P-V) diagram, where:
- The y-axis represents the Pressure (in \( \times 10^5 \, \text{Pa} \)).
- The x-axis represents the Volume (in \( \text{m}^3 \)).

The process described involves a gas expanding:
- From point A (4.0 \( \times 10^5 \, \text{Pa} \), 0.30 \( \text{m}^3 \))
- To point B (2.0 \( \times 10^5 \, \text{Pa} \), 0.75 \( \text{m}^3 \))

The graph consists of two linear segments:
1. From (4.0 \( \times 10^5 \, \text{Pa} \), 0.30 \( \text{m}^3 \)) to (2.0 \( \times 10^5 \, \text{Pa} \), 0.60 \( \text{m}^3 \))
2. From (2.0 \( \times 10^5 \, \text{Pa} \), 0.60 \( \text{m}^3 \)) to (2.0 \( \times 10^5 \, \text{Pa} \), 0.75 \( \text{m}^3 \))

#### Calculation:
To find the work done \( W \) by the gas, we calculate the area under the P-V curve.

1. **First Segment (A to midpoint):**
- Pressure \( P \) changes linearly from 4.0 \( \times 10^5 \, \text{Pa} \) to 2.0 \( \times 10^5 \, \text{Pa} \).
- Volume \( V \) changes from 0.30 \( \text{m}^3 \) to 0.60 \( \text{m}^3 \).

Area of this trapezoid:
\[
W_1

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