The temperature of two bodies measured by a thermometer are `t_1=20^@C pm 0.5^@C ` and `t_2=50^@C pm 0.5^@C` . Calculate the temperature difference and error there in .

Options

A. `30^(@)C+-1^(@)C`
B. `70^(@)C+-0.5^(@)C`
C. `30^(@)C+-0.5^@C`
D. `70^(@)C+-1^(@)C`

Explanation

To solve the problem of calculating the temperature difference and the associated error between two bodies measured by a thermometer, we will follow these steps:

### Step 1: Identify the given temperatures and their uncertainties
We have:
- \( t_1 = 20^\circ C \pm 0.5^\circ C \)
- \( t_2 = 50^\circ C \pm 0.5^\circ C \)

### Step 2: Calculate the temperature difference
The temperature difference \( \Delta t \) can be calculated using the formula:
\[ \Delta t = t_2 - t_1 \]
Substituting the values:
\[ \Delta t = 50^\circ C - 20^\circ C = 30^\circ C \]

### Step 3: Calculate the error in the temperature difference
The error in the temperature difference \( \Delta T \) is calculated by adding the absolute errors of the two measurements:
\[ \Delta T = \Delta t_1 + \Delta t_2 \]
Where:
- \( \Delta t_1 = 0.5^\circ C \)
- \( \Delta t_2 = 0.5^\circ C \)

Substituting the values:
\[ \Delta T = 0.5^\circ C + 0.5^\circ C = 1^\circ C \]

### Step 4: Present the final result
The final result for the temperature difference with its error can be expressed as:
\[ \Delta t = 30^\circ C \pm 1^\circ C \]

### Final Answer:
The temperature difference is \( 30^\circ C \pm 1^\circ C \).

---