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:
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:
Show Hint
- Use linear conversion formulas when correlating temperature scales.
Updated On: June 02, 2025
- \( 0^o C \)
- \( 50^o C \)
- \( 100^o C \)
- \( 150^o C \)
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The Correct Option is D
Solution and Explanation
Step 1: Establishing the correlation formula.
- 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).
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