# PV Diagram of Ideal Monatomic Gas Processes

• chopnhack
In summary, the gas undergoes a three-step process: it expands adiabatically from 588 K to 389 K, is compressed at constant pressure until its temperature reaches 3 K, and then returns to its original pressure and temperature by a constant volume process.
chopnhack

## Homework Statement

1.0 mol sample of an ideal monatomic gas originally at a pressure of 1 atm undergoes a 3-step process as follows:

It expands adiabatically from T1 = 588 K to T2 = 389 K

It is compressed at constant pressure until its temperature reaches T3 K

It then returns to its original pressure and temperature by a constant volume process.

a. Plot these processes on a PV diagram

b. Determine the temperature T3

c. Calculate the change in internal energy, work done by the gas and heat added to the gas for each of these three processes

d. Calculate the change in internal energy, work done by the gas and heat added to the gas for the complete cycle.

## Homework Equations

I have included on my work sheet.

## The Attempt at a Solution

Please see attached, I currently have a LATeX allergy ;-) I am stuck at the point of not knowing for sure if I have come to a logical conclusion. I have seen adiabatic charts before that have a second isotherm under the first. The wording of the problem leads me to believe that I have drawn the proper PV diagram. If this is the case, then part ii) would indicate that the gas should return to its initial volume, which means its getting compressed under constant pressure. If that is the case, the gas must be losing heat. At least that is what I posited. My next thought was to continue with Charles Law since pressure is constant. Have I got it right or have I wasted half a day and two pages?

Thanks for any input.

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chopnhack
Chestermiller said:
I tried to upload the word file, but I guess it wasn't allowed. Let me try pdf.

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Thanks. So far, what you've done is OK. You can continue with Charles law, knowing that V3=V1. This will give you T3.

chopnhack
Chestermiller said:
Thanks. So far, what you've done is OK. You can continue with Charles law, knowing that V3=V1. This will give you T3.
That is a load off of my chest. I thought I was right, but with 1/2 a days work in this I didn't want to proceed with a false assumption. Thanks!

## What is a PV diagram of an ideal monatomic gas?

A PV diagram of an ideal monatomic gas is a graphical representation of the relationship between pressure (P) and volume (V) during various processes, such as isothermal, adiabatic, and isobaric processes.

## What is an ideal monatomic gas?

An ideal monatomic gas is a theoretical gas that consists of a single atom per molecule and has no intermolecular forces. It follows the ideal gas law, which states that the pressure, volume, and temperature of the gas are related by the equation PV = nRT, where n is the number of moles and R is the gas constant.

## What is the significance of the PV diagram in thermodynamics?

The PV diagram is an important tool in thermodynamics as it helps to visualize the changes in pressure and volume of a gas during different processes. It also allows for the calculation of work done by the gas, which is essential in understanding the energy transfer in a system.

## How does a PV diagram of an ideal monatomic gas differ from a real gas?

A PV diagram of an ideal monatomic gas assumes that the gas molecules have no volume and do not interact with each other. In reality, real gases have molecular interactions and non-zero volumes, which can affect their behavior and the shape of their PV diagrams.

## How can the first and second laws of thermodynamics be applied to a PV diagram of an ideal monatomic gas?

The first law of thermodynamics, which states that energy cannot be created or destroyed but can only be transferred, can be applied to a PV diagram by calculating the work done by the gas during a process. The second law of thermodynamics, which states that the total entropy of a closed system cannot decrease, can be applied by analyzing the direction of the processes on the PV diagram, as they must follow a path of increasing entropy.

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