The initial and final temperatures are recorded as `(40.6 +- 0.3)^@C `and `(50.7+-0.2)^@C`. The rise in temperature is

Options

A. `10.1^@C`
B. `(10.1 +- 0.3)^(0)C`
C. `(10.1 +- 0.5)^(@)C`
D. `(10.1 +- 0.1)^(@)C`

Answer

To solve the problem of calculating the rise in temperature given the initial and final temperatures with their uncertainties, we will follow these steps:

### Step 1: Identify the Initial and Final Temperatures
- Initial Temperature (T_initial) = \(40.6 \pm 0.3\) °C
- Final Temperature (T_final) = \(50.7 \pm 0.2\) °C

### Step 2: Calculate the Rise in Temperature
The rise in temperature (ΔT) can be calculated using the formula:
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]
Substituting the values:
\[ \Delta T = (50.7) - (40.6) = 10.1 \text{ °C} \]

### Step 3: Calculate the Uncertainty in the Rise in Temperature
When subtracting two measurements with uncertainties, the uncertainties are added together. Therefore, we will add the uncertainties of the initial and final temperatures:
\[ \text{Uncertainty in } \Delta T = \text{Uncertainty in } T_{\text{final}} + \text{Uncertainty in } T_{\text{initial}} = 0.2 + 0.3 = 0.5 \text{ °C} \]

### Step 4: Combine the Results
Now, we can combine the calculated rise in temperature with its uncertainty:
\[ \Delta T = 10.1 \pm 0.5 \text{ °C} \]

### Final Answer
The rise in temperature is:
\[ \Delta T = 10.1 \pm 0.5 \text{ °C} \]

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