PV diagram, ranking heat transfer between 4 processes

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.
  • #1
HoboBones
7
1
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
Apologies, made a mistake when posting. Please see below post.
 
Last edited:
Physics news on Phys.org
  • #2
Problem and pV diagram

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

Screenshot 2022-12-04 at 5.36.46 PM.png

Given pV diagram
Screenshot 2022-12-04 at 5.24.58 PM.png

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!
 

Attachments

  • Screenshot 2022-12-04 at 5.24.58 PM.png
    Screenshot 2022-12-04 at 5.24.58 PM.png
    7.1 KB · Views: 60
  • Screenshot 2022-12-04 at 5.34.48 PM.png
    Screenshot 2022-12-04 at 5.34.48 PM.png
    10.4 KB · Views: 55
  • Screenshot 2022-12-04 at 5.35.38 PM.png
    Screenshot 2022-12-04 at 5.35.38 PM.png
    9.3 KB · Views: 47
  • #3
##dW=pdV.## Replace ##p## using the ideal gas law and integrate. Note that "isothermal" means "constant ##T##."
 
  • #4
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
 
  • #5
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
 
  • #6
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.
 

Related to PV diagram, ranking heat transfer between 4 processes

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.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
841
  • Introductory Physics Homework Help
Replies
1
Views
937
  • Introductory Physics Homework Help
Replies
2
Views
745
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Materials and Chemical Engineering
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
5K
  • Engineering and Comp Sci Homework Help
Replies
22
Views
2K
Back
Top