Calculating Change in Energy: A Graph Analysis

In summary, the conversation discusses finding the magnitude of the IF vector and calculating the change in internal energy and heat added for a direct path from I to A. The relevant equation to use is ΔW=pΔV, and the heat added QIF is given. Alternatively, the first law can be applied for the direct path. The conversation concludes with the person saying they have figured it out and thanking for the help.
  • #1
RandiSS
5
1
Homework Statement
A gas expands from I to F in the figure. The energy added to the gas by heat is 486 J when the gas goes from I to F along the diagonal path.

1. What is the change in internal energy of the gas?
Answer in units of J.
2. How much energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy? Answer in units of J.
Relevant Equations
ΔU = Q + W
W=pΔV
Not a solution. This is the graph provided.
1E14D1B0-D638-4A92-9F84-6C6655F9A660.jpeg

I think I start with finding the magnitude of the IF vector but I’m not sure. And I don’t know where to go from there.
 
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  • #2
Can you at least calculate the change in internal energy and heat added to go from I to A?
 
  • #3
Alternatively, apply the first law for the direct path IF. You are given the heat added QIF and you are looking for the change in internal energy ΔUIF. Can you find WIF from the graph? Note that your relevant equation should be ΔW=pΔV.
 
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Likes Chestermiller
  • #4
kuruman said:
Alternatively, apply the first law for the direct path IF. You are given the heat added QIF and you are looking for the change in internal energy ΔUIF. Can you find WIF from the graph? Note that your relevant equation should be ΔW=pΔV.
Hey I got it figured out. Thanks for the help. :)
 

FAQ: Calculating Change in Energy: A Graph Analysis

What is the primary purpose of analyzing a graph to calculate change in energy?

The primary purpose of analyzing a graph to calculate change in energy is to visually interpret and quantify the energy transformations or transfers within a system over a given period or under varying conditions. This helps in understanding the dynamics of the system and in making predictions or optimizations based on the observed data.

How do you identify the initial and final energy states on a graph?

The initial and final energy states on a graph are typically identified by locating the points on the graph that correspond to the starting and ending conditions of the system being analyzed. These points are often marked on the x-axis (time or another independent variable) and the y-axis (energy). The difference between these two points represents the change in energy.

What types of graphs are commonly used for energy analysis?

Common types of graphs used for energy analysis include line graphs, bar graphs, and scatter plots. Line graphs are particularly useful for showing changes over time, while bar graphs can effectively compare different states or conditions. Scatter plots are useful for identifying correlations between variables.

How can you calculate the area under a curve on a graph to determine energy change?

To calculate the area under a curve on a graph, which often represents the total energy change, you can use numerical integration methods such as the trapezoidal rule or Simpson's rule. These methods approximate the area by dividing it into smaller, manageable segments and summing their areas to get an overall estimate.

What are some common sources of error when calculating energy change from a graph?

Common sources of error when calculating energy change from a graph include inaccurate data points, incorrect identification of initial and final states, and errors in numerical integration methods. Additionally, external factors not accounted for in the graph, such as environmental changes or measurement inaccuracies, can also contribute to errors.

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