The steam point and the ice point of a mercury thermometer are marked as `80^@ and 10^@`. At what temperature on centigrade scale the reading of this thermometer will be `59^@` ?

Explanation

To find the temperature on the centigrade scale corresponding to a reading of 59° on a mercury thermometer marked with steam and ice points at 80° and 10° respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Known Values:**
- Ice point (L0) = 10°
- Steam point (L100) = 80°
- Reading on the thermometer (L1) = 59°

2. **Use the Linear Interpolation Formula:**
The formula to convert the thermometer reading to the centigrade scale is given by:
\[ T = \frac{L1 - L0}{L100 - L0} \times 100 \]
Where:
- \( T \) is the temperature in degrees Celsius.
- \( L1 \) is the thermometer reading.
- \( L0 \) is the ice point.
- \( L100 \) is the steam point.

3. **Substitute the Values:**
Plugging in the known values into the formula:
\[ T = \frac{59 - 10}{80 - 10} \times 100 \]

4. **Calculate the Numerator:**
Calculate \( L1 - L0 \):
\[ 59 - 10 = 49 \]

5. **Calculate the Denominator:**
Calculate \( L100 - L0 \):
\[ 80 - 10 = 70 \]

6. **Substitute Back into the Formula:**
Now substitute the results back into the formula:
\[ T = \frac{49}{70} \times 100 \]

7. **Perform the Division:**
Calculate \( \frac{49}{70} \):
\[ \frac{49}{70} = 0.7 \]

8. **Multiply by 100:**
Finally, multiply by 100 to find the temperature in degrees Celsius:
\[ T = 0.7 \times 100 = 70° \]

### Final Answer:
The temperature on the centigrade scale corresponding to a reading of 59° on the thermometer is **70° Celsius**.

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