The temperature of two bodies measured by a thermometer are `(2.1 +-0.5)^(@)C` and `(50+-0.5)^(@)C`. Calculate the temperature difference with error limits.

Explanation

To solve the problem of calculating the temperature difference between two bodies along with their error limits, we can follow these steps:

### Step 1: Write down the given values
We have two temperatures measured with their respective uncertainties:
- \( T_1 = 2.1 \pm 0.5 \, ^\circ C \)
- \( T_2 = 50 \pm 0.5 \, ^\circ C \)

### Step 2: Calculate the temperature difference
The temperature difference \( T \) between the two bodies is calculated as:
\[ T = T_2 - T_1 \]
Substituting the values:
\[ T = 50 - 2.1 = 47.9 \, ^\circ C \]

### Step 3: Calculate the error in the temperature difference
The error in the temperature difference, denoted as \( \Delta T \), is found by adding the absolute uncertainties of the two measurements:
\[ \Delta T = \Delta T_2 + \Delta T_1 \]
Given that both uncertainties are \( 0.5 \, ^\circ C \):
\[ \Delta T = 0.5 + 0.5 = 1.0 \, ^\circ C \]

### Step 4: Combine the temperature difference with its error limits
Now we can express the temperature difference with its error limits:
\[ T = 47.9 \pm 1.0 \, ^\circ C \]

### Final Answer
The temperature difference between the two bodies with error limits is:
\[ 47.9 \pm 1.0 \, ^\circ C \]

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