Let's clarify the step-by-step calculation for the sum of squared errors (SSE) for the data collected by both students.

### Constants
- \( R = 8.3 \, \text{J/(K·mol)} \)
- \( V = 16.6 \, \text{m}^3/\text{mol} \)
- \( n = 1 \, \text{mol} \)

### Ideal Gas Law
\[ P = \frac{nRT}{V} \]

### Predicted Pressures Using Ideal Gas Law
\[ P = \frac{8.3 \times T}{16.6} = 0.5 \times T \]

### Data Collected by Student A
| \( T(K) \) | 274 | 276 | 278 | 282 | 290 |
|------------|-----|-----|-----|-----|-----|
| \( P(Pa) \) | 137 | 139 | 142 | 141 | 142 |

### Data Collected by Student B
| \( T(K) \) | 276 | 280 | 284 | 288 | 290 |
|------------|-----|-----|-----|-----|-----|
| \( P(Pa) \) | 137 | 141 | 142 | 148 | 145 |

#### Step-by-Step Calculation for Student A

1. Calculate the predicted pressures using \( P = 0.5 \times T \):
   - For \( T = 274 \): \( P = 0.5 \times 274 = 137 \)
   - For \( T = 276 \): \( P = 0.5 \times 276 = 138 \)
   - For \( T = 278 \): \( P = 0.5 \times 278 = 139 \)
   - For \( T = 282 \): \( P = 0.5 \times 282 = 141 \)
   - For \( T = 290 \): \( P = 0.5 \times 290 = 145 \)

2. Calculate the errors by subtracting the observed pressures from the predicted pressures:
   - Error for \( T = 274 \): \( 137 - 137 = 0 \)
   - Error for \( T = 276 \): \( 139 - 138 = 1 \)
   - Error for \( T = 278 \): \( 142 - 139 = 3 \)
   - Error for \( T = 282 \): \( 141 - 141 = 0 \)
   - Error for \( T = 290 \): \( 142 - 145 = -3 \)

3. Square each error:
   - \( 0^2 = 0 \)
   - \( 1^2 = 1 \)
   - \( 3^2 = 9 \)
   - \( 0^2 = 0 \)
   - \( (-3)^2 = 9 \)

4. Sum the squared errors to get the SSE:
   - SSE for Student A: \( 0 + 1 + 9 + 0 + 9 = 19 \)

#### Step-by-Step Calculation for Student B

1. Calculate the predicted pressures using \( P = 0.5 \times T \):
   - For \( T = 276 \): \( P = 0.5 \times 276 = 138 \)
   - For \( T = 280 \): \( P = 0.5 \times 280 = 140 \)
   - For \( T = 284 \): \( P = 0.5 \times 284 = 142 \)
   - For \( T = 288 \): \( P = 0.5 \times 288 = 144 \)
   - For \( T = 290 \): \( P = 0.5 \times 290 = 145 \)

2. Calculate the errors by subtracting the observed pressures from the predicted pressures:
   - Error for \( T = 276 \): \( 137 - 138 = -1 \)
   - Error for \( T = 280 \): \( 141 - 140 = 1 \)
   - Error for \( T = 284 \): \( 142 - 142 = 0 \)
   - Error for \( T = 288 \): \( 148 - 144 = 4 \)
   - Error for \( T = 290 \): \( 145 - 145 = 0 \)

3. Square each error:
   - \( (-1)^2 = 1 \)
   - \( 1^2 = 1 \)
   - \( 0^2 = 0 \)
   - \( 4^2 = 16 \)
   - \( 0^2 = 0 \)

4. Sum the squared errors to get the SSE:
   - SSE for Student B: \( 1 + 1 + 0 + 16 + 0 = 18 \)

So, the SSE for Student A is 19, and for Student B, it is 18.

Would you like more details or have any other questions?

Here are 5 questions you can ask next:
1. Can you explain more about how to interpret SSE?
2. What if the gas constant \( R \) was different; how would that affect the calculations?
3. Are there any other methods to measure the goodness of fit besides SSE?
4. How does temperature affect the pressure in the ideal gas law?
5. Can you provide examples of when the ideal gas law might not be accurate?

Tip: Always check the units and constants used in your calculations to ensure accuracy and consistency.

Understand the calculation of Sum of Squared Errors (SSE) for data collected using the Ideal Gas Law. Detailed step-by-step analysis for Student A and Student B, including predictions, errors, and SSE calculations. Suitable for undergraduate students studying thermodynamics and data analysis.

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