How Much Heat Is Needed for Each Process in a PV Diagram?

In summary, the conversation was about a problem involving a monoatomic gas following a specific process, and the question of how much heat was needed for two different steps in the process. The conversation included calculations and equations to find the heat flow and temperature at different points in the process. The final solution involved using the ideal gas law and knowing the initial temperature to find the final temperature and ultimately determine the heat flow.
  • #1
Nellen2222
55
0

Homework Statement



A monoatomic gas follows the process 1--> 2---> 3---> shown in the figure. How much heat is needed for (a) process 1-->2, and b process 2-->3 ?

Link: http://www.chegg.com/homework-help/questions-and-answers/monatomic-gas-follows-process-1-2-3-shown-figure-heat-needed-1-2-process-2-3-process-q1077907

Homework Equations





The Attempt at a Solution



Well, Volume changes so work changes. I calculated the work from point 1 to point 2. The change in volume was 200cm^3 which is 0.0002m^3. The pressure in atmospheres is 3, converting that to pascals is 303,975Pa.

I multiplied them together to get the area under the graph for work : (303975Pa)(0.0002m^3)= 60.795J

So now I have work. But this for some reason is not the answer.The answer is actually 150J, I just don't understand what to d ofrom this point

I know that Eth=3/2nRΔT , but i don't have moles so what can I do from this equation? I just don't know where to g ofrom here. Please help! Thanks.
 
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  • #2
Nellen2222 said:

The Attempt at a Solution



Well, Volume changes so work changes. I calculated the work from point 1 to point 2. The change in volume was 200cm^3 which is 0.0002m^3. The pressure in atmospheres is 3, converting that to pascals is 303,975Pa.

I multiplied them together to get the area under the graph for work : (303975Pa)(0.0002m^3)= 60.795J

So now I have work. But this for some reason is not the answer.The answer is actually 150J, I just don't understand what to d ofrom this point

I know that Eth=3/2nRΔT , but i don't have moles so what can I do from this equation? I just don't know where to g ofrom here. Please help! Thanks.
The process from 1-2 is a constant pressure expansion. So what is the heat flow in a constant pressure expansion (hint: what is Cp for a monatomic gas?).

Without knowing Cp you can work this out using the first law and the ideal gas law: (1) Q = ΔU + W = ΔU + PΔV = nCvΔT + nRΔT for a constant pressure process.

AM
 
  • #3
I don't understand what youre trying to say. Cp for a monoatomic gas is 20.8. How does that formula help me at al? I stil don't have moles, or ΔT at point 2.

Elaborate please..?

As far as I can see i have 3 unknowns. Q, n, and T for point 2. I still don't get where to go after calcilating work. I know i have to add q+w, I just don't know how to get Q.
 
  • #4
Nellen2222 said:
I don't understand what youre trying to say. Cp for a monoatomic gas is 20.8. How does that formula help me at al? I stil don't have moles, or ΔT at point 2.

Elaborate please..?
Assume you have one mole ie. that the question is asking for the amount of heat flow per mole.

From the ideal gas law PΔV = RΔT for a constant volume process. So ΔT = PΔV/R. The heat flow per mole is just Q = CpΔT.

As far as I can see i have 3 unknowns. Q, n, and T for point 2. I still don't get where to go after calcilating work. I know i have to add q+w, I just don't know how to get Q.
Why are you interested in the work? 1-2 is at constant P and 2-3 is at constant volume. If you want to determine Q just use Cp and Cv. All you have to do is find ΔT. I'll let you figure out the ΔT for the constant volume process.

AM
 
  • #5
T is 60.795J/20.8 = 2.92 mol*k ... don't see where this is going still? for 1--2 the answer is 150J, I am still not seeing it..
 
Last edited:
  • #6
You know the temperature in state 1. Use the ideal gas law to determine the amount of gas. With the ideal gas law, you also find the temperature in state 2.

ehild
 
  • #7
Im not getting it... your saying I know heat at point 1 which is 100deg celcius i agree, i find heat at point 2 with the ideal gas law and i get 74.6K at point 2... now what... Its been hours, can you please direct me withalot more clarity so I can move on with my life?
 
  • #8
Nellen2222 said:
Im not getting it... your saying I know heat at point 1 which is 100deg celcius i agree, i find heat at point 2 with the ideal gas law and i get 74.6K at point 2... now what... Its been hours, can you please direct me withalot more clarity so I can move on with my life?

T2 is not 74.6 K. According to the ideal gas law, P1V1/T1=P2V2/T2. P1=P2 so T2/T1=V2/V1. V1=100 cm3, V2=300 cm3 and T1=373 K. What is T2?

ehild
 

FAQ: How Much Heat Is Needed for Each Process in a PV Diagram?

How do you find heat from a PV diagram?

To find heat from a PV diagram, you can use the formula Q = ΔU + W, where Q is the heat, ΔU is the change in internal energy, and W is the work done.

What is the relationship between heat and a PV diagram?

The relationship between heat and a PV diagram is that heat is represented by the area under the curve on a PV diagram. This area represents the work done by the system.

Can you determine the heat transfer from a PV diagram?

Yes, you can determine the heat transfer from a PV diagram by calculating the area under the curve on the diagram. This area represents the work done, which is equal to the heat transfer.

How can you use a PV diagram to analyze heat transfer?

A PV diagram can be used to analyze heat transfer by calculating the area under the curve, which represents the work done. This value can then be used to determine the heat transfer using the formula Q = ΔU + W.

What other information is needed to find heat from a PV diagram?

In addition to the PV diagram, you will also need the initial and final states of the system. This includes the initial and final pressure and volume, as well as any other relevant information such as the gas type and temperature.

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