# Drawing a PV Diagram: Solving Homework w/ Work Calculation

• imatreyu
In summary, the gas does work to expand and contract isothermally, but the work done is not consistent throughout the entire cycle.

## Homework Statement

One mole of an ideal gas at an inital tempreature of 300K and pressure of 4 atm is carried through the following reversible cycle:

a) It expands isothermally until its volume is doubled.
b) It is compressed to its original volume at constant pressure.
c) It is compressed isothermally to a pressure of 4 atm.
d) It expands at constant pressure to its original volume

Make a plot of this cycle process on a PV diagram and calculate the work done by the gas per cycle.

## The Attempt at a Solution

Okay so step a. means that while Vo goes to 2Vo the pressure doubles as well, yes? And step b means that the pressure is the same but the volume goes to Vo. And so then step C should mean that since P is returning to its initial, the gas returns to Vo too, right? But if that's true, then D doesn't make sense since it has already returned to Vo.

Please help! Once I get the diagram correct, I'm just going to use the area to find the work done.

imatreyu said:
Okay so step a. means that while Vo goes to 2Vo the pressure doubles as well, yes?

Take a look at the PV = nRT equation. If T is held constant (isothermal), how must P and V relate to each other?

And step b means that the pressure is the same but the volume goes to Vo. And so then step C should mean that since P is returning to its initial, the gas returns to Vo too, right?

Again, take a look at PV = nRT. What's the current volume and pressure when step C begins? How do P and V vary when the compression (or expansion) is isothermal?

Oh okay haha. . .P has to be half. . .

Thank you :)

## 1. What is a PV diagram?

A PV diagram, also known as a pressure-volume diagram, is a graph that shows the relationship between pressure and volume for a gas or fluid. It is often used in thermodynamics to analyze the work done by a gas or fluid in a system.

## 2. How do you draw a PV diagram?

To draw a PV diagram, you will need to collect data on the pressure and volume of the gas or fluid in your system. Then, plot the data points on a graph with pressure on the y-axis and volume on the x-axis. Finally, connect the data points with a smooth curve to create the PV diagram.

## 3. What is the purpose of solving homework with work calculation using a PV diagram?

Using a PV diagram to solve homework problems involving work calculation allows you to visually understand the changes in pressure and volume of a gas or fluid in a system. It also helps you accurately calculate the work done by the gas or fluid.

## 4. What are the key components of a PV diagram?

The key components of a PV diagram include the axes (with pressure on the y-axis and volume on the x-axis), data points, and a curve representing the relationship between pressure and volume. It may also include labels and units for the axes and data points.

## 5. What are some common mistakes when drawing a PV diagram?

Some common mistakes when drawing a PV diagram include not plotting the data points accurately, not using the correct scale for the axes, and not connecting the data points with a smooth curve. It is also important to check that the units for pressure and volume match and to label the axes and data points correctly.