# PV diagram, ranking heat transfer between 4 processes

• HoboBones
In summary, Apologies, made a mistake when posting. Please see below post.Problem and pV diagram: Problem: Rank the magnitude of the heat transferred with the gas in each of the four processes.
HoboBones
Homework Statement
Rank the magnitude of the heat transferred with the gas in each of the four processes.
Relevant Equations
First law of thermodynamics
Thermal energy
Ideal gas law
Work done by gas
Work in isothermal

Last edited:
Problem and pV diagram

Problem: Rank the magnitude of the heat transferred with the gas in each of the four processes.

Given pV diagram

Attempt at solution with my questions in red

Equations used:

Thermal energy: Eth=3/2nRT
Ideal gas law: pV=nRT
Workby gas=area under curve
Work in isothermal: Wgas,isothermal=nRTln(Vf/Vi)
First law of thermodynamics applied to gases: ΔEth=Q-Wgas

Set up:

From ideal gas law, pV=nRT. Thus,

ΔEth=3/2nRT=3/2pV
Wgas, isothermal=nRTln(Vf/Vi)=pVln(Vf/Vi)
ΔEth=Q-Wgas --> Q=ΔEth+Wgas

Solving for ΔEth, Wgas, and |Q| for the processes: (I don't understand why we are solving for absolute value of Q)

I need some help solving for ΔE, Wgas, and |Q| for process 3->4

 Process​ ΔEth​ Wgas​ |Q|​ 1->2​ -9pV​ -6pV​ 15pV​ 2->3​ 3/2(-pV)​ 0​ 1.5pV​ 3->4​ 0pV​ ?​ ?​ 4->5​ 3/2(pV)​ pV​ 2.5pV​

Here is my attempt at process 3->4

ΔEth3->4 = 3/2(2pV-2pV) = 0 (My professor has the answer as "0pV" and not 0, not sure why?

Wgas,isothermal= area under the curve?

Area of triangle + Area under rectangle = 2pV? (correct answer is -pVln(Vf/Vi)

|Q| = -pVln(2V/V) = 1.4pV (I am not sure how this is the correct answer)

Any help would be much appreciated!

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##dW=pdV.## Replace ##p## using the ideal gas law and integrate. Note that "isothermal" means "constant ##T##."

Update, I think I figured it out but not really understanding

For process 3->4,

Wgas,isothermal = area under curve = 1/2bh + Arectangle = 2pV

We can plug in our area into the work in isothermal equation, thus

Wgas,isothermal = -pVln(Vf/Vi) = -2pVln(2V/V)

|Q| = ΔEth(3->4) + Wgas,isothermal = 0pV -2pVln(2V/V) = |-1.386pV| = 1.4pV

kuruman said:
##dW=pdV.## Replace ##p## using the ideal gas law and integrate. Note that "isothermal" means "constant ##T##."
She doesn't want us to use integrals unfortunately

Integrals was plan A. Plan B says call the heat entering the gas during the isothermal part ##Q_{34}.## Add an extra row to the table that completes the cycle from 5 to 1 with an isochoric process. Calculate the new entries the same way you did step 2 to 3. Now add all 5 elements in each column. Note that ##W_{34}=Q_{34}## so you have one equation and one unknown, ##Q_{34}.## There is no plan C.

## 1. What is a pV diagram?

A pV diagram, also known as a pressure-volume diagram, is a graphical representation of the relationship between pressure and volume for a gas or fluid. It is a useful tool for understanding thermodynamic processes and analyzing the work done by or on a system.

## 2. How do you interpret a pV diagram?

In a pV diagram, the x-axis represents volume and the y-axis represents pressure. The shape of the curve on the diagram can indicate the type of process (isothermal, adiabatic, etc.) and the area under the curve represents the work done by or on the system.

## 3. What are the 4 processes represented on a pV diagram?

The 4 processes commonly represented on a pV diagram are isothermal, adiabatic, isobaric, and isochoric. In an isothermal process, the temperature remains constant. In an adiabatic process, there is no heat transfer. In an isobaric process, the pressure remains constant. In an isochoric process, the volume remains constant.

## 4. How do you rank heat transfer between the 4 processes on a pV diagram?

The amount of heat transferred in each process can be ranked by looking at the area under the curve on the pV diagram. The larger the area, the more heat is transferred. For example, in an isobaric process, the area under the curve represents the work done by the system, which is equal to the heat transferred.

## 5. What are some real-life applications of pV diagrams?

pV diagrams are commonly used in thermodynamics and engineering to analyze and design systems such as engines, refrigerators, and heat pumps. They are also used in meteorology to study atmospheric processes and in chemistry to understand gas behavior.

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