Question

In an alcohol-in-glass thermometer, the alcohol column has length 12.66 cm at 0.0 ∘C and length 22.49 cm at 100.0 ∘C. Part A What is the temperature if the column has length 18.77 cm ? Express your answer using four significant figures. T = nothing ∘C Request Answer Part B What is the temperature if the column has length 14.23 cm ? Express your answer using four significant figures.

Answer 1

Answer:

$62.1566632757\ ^{\circ}C$

$15.9715157681\ ^{\circ}C$

Explanation:

$\Delta T$ = Change in termperature

$\Delta L$ = Change in length

We have the relation

$\dfrac{\Delta L}{\Delta T}=\dfrac{22.49-12.66}{100-0}=\dfrac{18.77-12.66}{t-0}\\\Rightarrow t=\dfrac{18.77-12.66}{0.0983}\\\Rightarrow t=62.1566632757\ ^{\circ}C$

The temperature is $62.1566632757\ ^{\circ}C$

$\dfrac{\Delta L}{\Delta T}=\dfrac{22.49-12.66}{100-0}=\dfrac{14.23-12.66}{t-0}\\\Rightarrow t=\dfrac{14.23-12.66}{0.0983}\\\Rightarrow t=15.9715157681\ ^{\circ}C$

The temperature is $15.9715157681\ ^{\circ}C$

Answer 2

(A) When the length is 18.77 cm, the temperature will be "62.2°C".

(B) When the length is 14.23 cm, the temperature will be "15.98°C".

(A)

According to the question,

The change in length will be:

= $l_2-l_1$

= $22.49-12.66$

= $9.83 \ cm$

The change per degree will be:

= $\frac{Change \ in \ length}{Temperature}$

= $\frac{9.83}{100}$

= $0.0983 \ cm/deg$

Now,

The change in length,

= $18.77-12.66$

= $6.11 \ cm$

hence,

The temperature,

= $\frac{6.11}{0.0983}$

= $62.2^{\circ} C$

(B)

The change in length,

= $14.23-12.66$

= $1.57 \ cm$

hence,

The temperature will be:

= $\frac{1.57}{0.0983}$

= $15.98^{\circ} C$

Thus the above answers are correct.

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