Math Problem Statement

Solution

From the extracted text, we have the following data and options:

Data Collected by Student A:

T(K)T(K)274276278282290
P(Pa)P(Pa)137139142141142

Data Collected by Student B:

T(K)T(K)276280284288290
P(Pa)P(Pa)137141142148145

Options to Choose:

  • A has a better fit than B.
  • B has a better fit than A.
  • A and B both have the same fit.
  • SSE calculated by B is 18.
  • SSE calculated by A is 14.
  • SSE calculated by both A and B is 18.

To determine which student has a better fit and the SSE values, we need to calculate the sum of squared errors (SSE) for both sets of data.

Using the ideal gas equation PV=nRTPV = nRT and knowing V=16.6m3/molV = 16.6 \, m^3/mol, R=8.3J/(Kmol)R = 8.3 \, J/(K \cdot mol), we can calculate the expected pressures and then compute the SSE for both students.

Let's proceed with these calculations.The calculated sum of squared errors (SSE) are as follows:

  • SSE for Student A: 19.0
  • SSE for Student B: 18.0

Based on these results, the correct options are:

  • B has a better fit than A.
  • SSE calculated by B is 18.

Do you want more details or have any questions?

Here are 5 questions you can ask next:

  1. How is the sum of squared errors (SSE) calculated?
  2. Can you explain the ideal gas law in more detail?
  3. How do we interpret the fit quality based on SSE values?
  4. What other methods can be used to determine the best fit?
  5. How would changes in the gas constant R affect the results?

Tip: When analyzing experimental data, always consider potential sources of error and the assumptions made during calculations.

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Math Problem Analysis

Mathematical Concepts

Ideal Gas Law
Sum of Squared Errors (SSE)

Formulas

Ideal Gas Law: PV = nRT
Sum of Squared Errors (SSE) calculation

Theorems

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Suitable Grade Level

Undergraduate level