A platinum resistance thermometer reads `0^@ C` when its resistance is `80 Omega and 100^@ C` when its resistance is `90 Omega`. Find the temperature at which the resistance is `86 Omega`.

Explanation

To solve the problem of finding the temperature at which the resistance of a platinum resistance thermometer is 86 ohms, we can use the linear relationship between temperature and resistance. The formula we will use is:

\[ T = \frac{R_T - R_0}{R_{100} - R_0} \times 100 \]

Where:
- \( T \) is the temperature in degrees Celsius,
- \( R_T \) is the resistance at temperature \( T \),
- \( R_0 \) is the resistance at 0°C,
- \( R_{100} \) is the resistance at 100°C.

### Step 1: Identify the known values
From the problem statement:
- \( R_0 = 80 \, \Omega \) (Resistance at 0°C)
- \( R_{100} = 90 \, \Omega \) (Resistance at 100°C)
- \( R_T = 86 \, \Omega \) (Resistance we want to find the temperature for)

### Step 2: Substitute the known values into the formula
Now we substitute the known values into the formula:

\[ T = \frac{86 \, \Omega - 80 \, \Omega}{90 \, \Omega - 80 \, \Omega} \times 100 \]

### Step 3: Calculate the numerator and denominator
Calculate the numerator:

\[ 86 \, \Omega - 80 \, \Omega = 6 \, \Omega \]

Calculate the denominator:

\[ 90 \, \Omega - 80 \, \Omega = 10 \, \Omega \]

### Step 4: Substitute back into the formula
Now substitute these values back into the equation:

\[ T = \frac{6 \, \Omega}{10 \, \Omega} \times 100 \]

### Step 5: Simplify the fraction
Simplify the fraction:

\[ T = 0.6 \times 100 \]

### Step 6: Calculate the final temperature
Now calculate the final temperature:

\[ T = 60 \, °C \]

### Final Answer
The temperature at which the resistance is 86 ohms is \( 60 \, °C \).

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