A) \[{{78}^{\text{o}}}W\]
B) \[{{117}^{\text{o}}}W\]
C) \[{{200}^{\text{o}}}W\]
D) \[{{139}^{\text{o}}}W\]
Correct Answer: B
Solution :
In general, whenever we are to go from any known scale to any unknown scale, then we follow the equation (Temperature on known scale) \[\frac{\text{-(LFP}\,\text{for}\,\text{known}\,\text{scale)}}{{{\text{(UFP-LFP)}}_{\text{known}}}}\] (Temperature on unknown scale) \[\text{=}\frac{\text{-(LFP}\,\text{for}\,\,\text{unknown}\,\text{scale)}}{{{\text{(UFP-LFP)}}_{\text{known}}}}\] or\[\frac{39-0}{100-0}=\frac{t-39}{239-39}\]or\[t={{117}^{o}}W\] Note: LFP \[\to \]Lower fixed point UFP\[\to \] Upper fixed point Alternative: \[\begin{matrix} \text{10}{{\text{0}}^{\text{o}}}\text{C} \\ {} \\ {{\text{0}}^{\text{o}}}\text{C} \\ \end{matrix}\underline{\overline{\underset{\downarrow }{\overset{\uparrow }{\mathop{100}}}\,\text{division}\underset{\downarrow }{\overset{\uparrow }{\mathop{200}}}\,}}\,\begin{matrix} \begin{align} & \text{Now}\,\text{scale} \\ & \text{23}{{\text{9}}^{\text{o}}}\text{W} \\ \end{align} \\ \text{divisions} \\ \text{3}{{\text{9}}^{\text{o}}}\text{W} \\ \end{matrix}\] \[\therefore \]\[{{39}^{o}}C=39\times 2+39={{(78+39)}^{o}}W\] \[={{117}^{o}}W\]
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