A uniform thermometre scale is at steady state with its 0 cm mark at `20°C` and 100 cm mark at `100°C`. Temperature of the 60 cm mark is-

Options

A. `48^(@)C`
B. `68^(@)C`
C. `52^(@)C`
D. `58^(@)C`

Answer

To find the temperature at the 60 cm mark of the thermometer scale, we can follow these steps:

### Step 1: Understand the given information
- The thermometer scale has its 0 cm mark at 20°C.
- The 100 cm mark is at 100°C.

### Step 2: Calculate the temperature gradient
The temperature gradient can be calculated using the formula:
\[ \text{Temperature Gradient} = \frac{\text{Change in Temperature}}{\text{Change in Length}} \]
Here, the change in temperature is \(100°C - 20°C = 80°C\) and the change in length is \(100 \text{ cm} - 0 \text{ cm} = 100 \text{ cm}\).

So, the temperature gradient is:
\[ \text{Temperature Gradient} = \frac{80°C}{100 \text{ cm}} = 0.8°C/\text{cm} \]

### Step 3: Calculate the temperature at the 60 cm mark
To find the temperature at the 60 cm mark, we can use the temperature gradient:
\[ \text{Temperature at 60 cm} = \text{Initial Temperature} + (\text{Temperature Gradient} \times \text{Length}) \]
The initial temperature at the 0 cm mark is 20°C.

Substituting the values:
\[ \text{Temperature at 60 cm} = 20°C + (0.8°C/\text{cm} \times 60 \text{ cm}) \]
Calculating the multiplication:
\[ 0.8°C/\text{cm} \times 60 \text{ cm} = 48°C \]
Now, adding this to the initial temperature:
\[ \text{Temperature at 60 cm} = 20°C + 48°C = 68°C \]

### Final Answer
The temperature at the 60 cm mark is **68°C**.

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