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A mercury thermometer read 80^{\circ} \mathrm{C} when the mercury is at 5.2 \mathrm{~cm} mark and 60^{\circ} \mathrm{C}  when the mercury is at 3.9 \mathrm{~cm} mark. Find the temperature when the mercury level is at 2.6 \mathrm{~cm} mark is  4×10x. Find the value of x.

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

\mathrm{\quad \frac{l_{1}-l_{2}}{l_{1}-l_{3}}=\frac{\alpha l_{0}\left(\mathrm{~T}_{1}-\mathrm{T}_{2}\right)}{\alpha l_{0}\left(\mathrm{~T}_{1}-\mathrm{T}_{3}\right)}=\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{~T}_{1}-\mathrm{T}_{3}}}

\mathrm{or \: \quad \frac{5.2-3.9}{5.2-2.6}=\frac{80-60}{80-\mathrm{T}_{3}}}

\mathrm{1.3\left(80-\mathrm{T}_{3}\right)=2.6(20) \: or \: \mathrm{T}_{3}=40^{\circ} \mathrm{C}}

T=400C=4×100C

 

But it is given that T=4×10x0C

This means that x=1

Posted by

Ritika Harsh

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