How Do You Calculate Temperatures and Volumes in a Helium Gas PV Diagram Cycle?

Using 101.3 kPa gives 366 K for T(a), which is what I got.In summary, the conversation discussed the calculation of T(a), T(b), and V(c) in a cycly ABC where BC is an isothermal process, given the values of P(a) = P(c) = 1atm, P(b) = 2atm, and V(a) = V(b) = 3m^3. The equations used were PV = nRT and V = nRT/P, and the correct values were T(a) = 366K, T(b) = 2T(a), and V(c) = 6m^3.
  • #1
mrmonkah
24
0

Homework Statement


100 moles of very dilute He gas are taken through the cycly ABC, where BC is an isothermal process. If P(a) = P(c) = 1atm, P(b) = 2atm and V(a) = V(b) = 3m^3, Calculate T(a), T(b) and V(c)


Homework Equations


eq1. PV = nRT
eq2. V = nRT/P


The Attempt at a Solution


Am i right in thinking that i can plug in the values of P(a) and V(a) to get T(a) into eq1. and similarly for T(b)?

I have T(a) = 361k, T(b) = 722k and V(c) = 6m^3

This seems to straight forward to be correct... any help would be great.
 
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  • #2
mrmonkah said:

The Attempt at a Solution


Am i right in thinking that i can plug in the values of P(a) and V(a) to get T(a) into eq1. and similarly for T(b)?

I have T(a) = 361k, T(b) = 722k and V(c) = 6m^3

This seems to straight forward to be correct... any help would be great.
Looks good, though I'm getting slightly different values for T(a) and T(b). You might want to recheck your calculation, and if you don't get slightly different results post your calculation of T(a) here. You are correct that T(b) is 2T(a), and V(c) is correct as well.

Did you use R=8.206 x 10-5 atm·m3/(mol·K)?
 
  • #3
Hi Redbelly,

Ive submitted the work now. Unfortunately before seeing this post.

I actually converted my units to SI. And so used: R = 8.314J/(K mol)

Ive had some feed back in the past about sticking with the given units in some situations and not in others... and so i don't always head in the right direction. I am thinking in this example, stay with original units.

Cheers for the heads up.

Regards,
Dan
 
  • #4
No problem. Since you've submitted the work, I'll mention that I had gotten 366 K for T(a), so you were pretty close, only 1.3% off. I suspect you used the approximation 1 atm = 100 kPa, instead of the more accurate 1 atm = 101.3 kPa.
 
  • #5


Yes, you are correct in your approach. Plugging in the given values for P(a) and V(a) into eq1. will give you the value for T(a). Similarly, plugging in the values for P(b) and V(b) into eq1. will give you the value for T(b).

As for V(c), you can use eq2. to calculate it. Since the process from B to C is isothermal, the temperature remains constant and therefore, the value of T(b) can be used in eq2. along with the given values of P(c) and V(c) to solve for V(c).

Your calculated values seem reasonable, but it is always a good idea to double check your calculations and make sure you are using the correct units. Also, make sure to include units in your final answers. Good job!
 

Related to How Do You Calculate Temperatures and Volumes in a Helium Gas PV Diagram Cycle?

1. What is a PV diagram in thermal physics?

A PV diagram, also known as a pressure-volume diagram, is a graphical representation of the relationship between pressure and volume of a system in thermal physics. It is a useful tool for understanding the behavior of gases and other thermodynamic systems.

2. How are PV diagrams used in thermal physics?

PV diagrams are used to visually represent the changes in pressure and volume of a system as it undergoes various thermodynamic processes, such as isothermal, adiabatic, and isobaric processes. They also help in calculating the work done by or on the system and determining its efficiency.

3. What does the shape of a PV diagram indicate?

The shape of a PV diagram depends on the type of process being represented. For example, for an isothermal process, the graph is a hyperbola, while for an adiabatic process, it is a steep curve. The area under the curve represents the work done by the system, and the slope of the curve represents the pressure-volume ratio.

4. How can PV diagrams be used to analyze thermodynamic processes?

PV diagrams can be used to analyze thermodynamic processes by determining the change in internal energy, work, and heat transfer for a given system. By plotting different processes on the same diagram, it is possible to compare their efficiency and understand the energy transformations taking place.

5. Are PV diagrams applicable to all thermodynamic systems?

PV diagrams are most commonly used for ideal gases, but they can also be used for other thermodynamic systems, such as steam engines and refrigeration cycles. However, for non-ideal gases, the shape of the PV diagram may be different due to the presence of intermolecular forces and other factors.

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