Question

In a new temperature scale say \( ^oP \), the boiling and freezing points of water at one atmosphere are \( 100^o P \) and \( 300^o P \) respectively. Correlate this scale with the Centigrade scale. The reading of \( 0^o P \) on the Centigrade scale is:

• A. \( 0^o C \)
• B. \( 50^o C \)
• C. \( 100^o C \)
• D. \( 150^o C \)

Hint:

- Use linear conversion formulas when correlating temperature scales.

Answer 1

The Correct Option is D

Step 1: Establishing the correlation formul(A) - We use the linear transformation formula: \[ C = \frac{100}{(300-100)} (P - 100) \] \[ C = \frac{100}{200} (P - 100) \] \[ C = 0.5 (P - 100) \] Step 2: Calculating for \( 0^o P \). \[ C = 0.5 (0 - 100) = -50^o C \] Step 3: Selecting the correct option. 
Since \( 0^o P \) corresponds to \( -50^o C \), the correct answer is (D).