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

[Nellen2222]

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.

 

[Andrew Mason]

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

 

[Nellen2222]

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.

 

[Andrew Mason]

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

 

[Nellen2222]

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..

 

[ehild]

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

 

[Nellen2222]

Im not getting it... your saying I know heat at point 1 which is 100deg celsius 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?

 

[ehild]

Im not getting it... your saying I know heat at point 1 which is 100deg celsius 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