Thermal Properties of Matter - Result Question 5
5. On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are $39^{\circ} W$ and $239^{\circ} W$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39^{\circ} C$ on the Celsius scale?
[2008]
(a) $78^{\circ} W$
(b) $117^{\circ} W$
(c) $200^{\circ} W$
(d) $139^{\circ} W$
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Answer:
Correct Answer: 5. (b)
Solution:
- (b) For different temperature scales, we have
$\frac{x \text{ - L.F.P }}{\text{ U.F.P.- L.F.P. }}=$ constant
Where L.F.P $\Rightarrow$ Lower Fixed point
U.H.F. $\Rightarrow$ Upper fixed point
where $x$ is the measurement at that scale. Here, if $C$ and $W$ be the measurements on Celsius and $W$ scale then,
$\frac{C-0}{100-0}=\frac{W-39}{239-39}(\therefore C=39^{\circ} C)$
$\Rightarrow W=\frac{39 \times 200}{100}+39=78+39=117^{\circ} W$
