# Solving PV Graphs: Work, Heat, ΔU Questions

In summary: I missing something?Where is the problem you want to solve?In summary, ehild is trying to find out how to solve problems involving the first law of thermodynamics. She has read on Physicsforums.com and found some equations that she needs to use. She has also scavenged equations off of the internet. She is missing an important equation and wants to solve a problem to verify her understanding.
I'm sorry I cannot conform to the default format Physicsforums.com; it is because I do not even know the first step to solving these sorts of problems, I don't know which equations to use which is a major problem. Here are the types of questions I require understanding.
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An ideal gas goes through three processes (A>B>C>[A]) (Triangular form) (PV Chart)
How would I figure out The Q, W, and ΔU (internal energy) for A to B, B to C, C to A?
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On another graph using variables but this time with numerical values for P and V on the axis, how would I find the work done by a monatomic ideal gas as it expands from point A to point C along the path shown in the figure? Also, how much heat would be absorbed BY the gas during this process?
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Finding the net work, heat, and ΔU in another PV Graph with data on the axis-es?
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Calculating temperature, work, and/or internal energy in another PV Graph?
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Whether or not W, Q, or ΔU is positive(gained) or negative(released) in an ideal gas system as well as how those three (Q,W,..U) are related?
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I really wish to work on the problems myself, so I have only asked what procedures I should take.
Here is a list of equations I have scavenged.

ΔU = Won + Q

ΔU = (3/2)nRΔT

Won = -PΔV

P1V1 = P2V2

(P1V1)/T2 = (P2V2)/T2

PV = nRT

Is there any important equation that I am missing?

A couple of errors it seems are to be found on the website but it has been very helpful so far I've read. Thank you ehild. :)

I'm sorry I cannot conform to the default format Physicsforums.com; it is because I do not even know the first step to solving these sorts of problems, I don't know which equations to use which is a major problem. Here are the types of questions I require understanding.
-
An ideal gas goes through three processes (A>B>C>[A]) (Triangular form) (PV Chart)
How would I figure out The Q, W, and ΔU (internal energy) for A to B, B to C, C to A?
These problems are all about the First Law of Thermodynamics:

ΔU = Q + W where W is the work done ON the gas. I prefer to use:

Q = ΔU + W where W is the work done BY the gas.

To determine the values, we would need to see the exact problem.

On another graph using variables but this time with numerical values for P and V on the axis, how would I find the work done by a monatomic ideal gas as it expands from point A to point C along the path shown in the figure? Also, how much heat would be absorbed BY the gas during this process?
Again, this requires application of the first law of thermodynamics.

From the PV diagram you can determine T (if you are given n or an initial T) and W = PΔV (or -PΔV, depending on which version of the first law you are using). From T you can determine ΔU using ΔU = nCvΔT (you have given this equation for a monatomic ideal gas where Cv = 3R/2). From W and ΔU you can determine Q.

AM

I understand your frustration with solving PV graphs. These types of problems require a strong understanding of thermodynamics and the relationships between pressure, volume, temperature, work, heat, and internal energy. I will provide some general steps and equations that can help you solve these types of problems, but it is important to note that different problems may require different approaches and equations. It is always best to review the specific problem and consider which equations are most relevant.

1. Identify the given information and variables:
The first step in solving any problem is to identify the given information and variables. In the case of PV graphs, this includes the pressure, volume, and temperature values at different points on the graph, as well as any other relevant information such as the type of gas or the specific path of the process.

2. Use the ideal gas law:
The ideal gas law, PV = nRT, is a fundamental equation that relates pressure, volume, temperature, and number of moles of an ideal gas. This equation can be rearranged to solve for any variable, depending on what information is given in the problem.

3. Use the first law of thermodynamics:
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the work (W) done on the system plus the heat (Q) absorbed by the system. This equation can be written as ΔU = Q - W. In solving PV graph problems, this equation is often used to calculate the change in internal energy between different points on the graph.

4. Calculate the work done:
To calculate the work done on the system, you can use the equation W = -PΔV, where P is the pressure and ΔV is the change in volume. This equation can be applied to different paths on the PV graph to calculate the work done during a specific process.

5. Calculate the heat absorbed:
To calculate the heat absorbed by the system, you can use the equation Q = nCΔT, where n is the number of moles of the gas and C is the specific heat capacity at constant volume. This equation can also be applied to different paths on the PV graph to calculate the heat absorbed during a specific process.

6. Consider the sign conventions:
It is important to pay attention to the sign conventions when calculating work, heat, and internal energy. Work done on the system is considered positive, while work done by the system is

## 1. What are PV graphs and why are they important in science?

PV graphs, or pressure-volume graphs, are visual representations of the relationship between pressure and volume in a system. They are important in science because they provide a way to analyze and understand thermodynamic processes, such as work, heat, and changes in internal energy.

## 2. How do you solve PV graphs for work?

To solve for work on a PV graph, you can use the formula W = PΔV, where W is work, P is pressure, and ΔV is the change in volume. This formula represents the area under the curve on the graph, which can be calculated using basic geometry or by breaking the graph into smaller shapes and adding their areas together.

## 3. How is heat represented on a PV graph?

Heat is represented on a PV graph as the change in internal energy (ΔU). This change in internal energy can be calculated by finding the difference between the final and initial points on the graph and multiplying by the gas constant (R).

## 4. What is the relationship between work, heat, and changes in internal energy on a PV graph?

The relationship between work, heat, and changes in internal energy on a PV graph is represented by the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the work done on the system (W) plus the heat transferred into the system (Q). This can be shown on a PV graph by the change in internal energy being equal to the sum of the areas of the work and heat curves.

## 5. How can you use PV graphs to analyze and understand thermodynamic processes?

PV graphs can be used to analyze and understand thermodynamic processes by providing a visual representation of the changes in pressure, volume, work, heat, and internal energy in a system. By examining the shape and slope of the graph, one can determine the efficiency and direction of a process, as well as the amount of work and heat involved. PV graphs can also be used to compare different processes and predict the behavior of a system under different conditions.

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