91影视

• The first temperature value is\({T_1} = 0^\circ {\rm{C}}\).
• The second temperature value is\({T_2} = 100^\circ {\rm{C}}\).
• The first length of the alcohol column is\({l_1} = 12.61{\rm{ cm}}\).
• The second length of the alcohol column is \({l_2} = 22.79{\rm{ cm}}\).

The temperature at the required length can be obtained with the help of the length of the alcohol column and the change in the temperature per unit length.

This change in temperature per unit column length is the ratio of the temperature difference to the difference of lengths.

The change in temperature per unit length can be expressed as

\(\Delta {T_{\rm{C}}} = \frac{{{T_2} - {T_1}}}{{{l_2} - {l_1}}}\).

Substitute the values in the above equation.

\(\begin{aligned}{c}\Delta {T_{\rm{C}}} &= \frac{{100^\circ {\rm{C}} - 0^\circ {\rm{C}}}}{{22.79{\rm{ cm}} - 12.61{\rm{ cm}}}}\\ &= 9.823^\circ {\rm{C/cm}}\end{aligned}\)

The temperature at a particular length can be expressed as

\(T\left( l \right) = {T_1} + \left( {l - {l_1}} \right)\left( {\Delta {T_{\rm{C}}}} \right)\).

Here, l is the new length of the column.

Substitute the values in the above equation.

\(T\left( l \right) = 0^\circ {\rm{C}} + \left( {l - 12.61{\rm{ cm}}} \right)\left( {9.823\;^\circ {\rm{C/cm}}} \right)\) 鈥� (i)

From equation (i), the temperature at the length of 18.70 cm can be calculated.

\(\begin{aligned}{c}T\left( {18.70{\rm{ cm}}} \right) &= 0^\circ {\rm{C}} + \left( {18.70{\rm{ cm}} - 12.61{\rm{ cm}}} \right)\left( {9.823\;^\circ {\rm{C/cm}}} \right)\\ &= 6.09{\rm{ cm}} \times \left( {9.823\;^\circ {\rm{C/cm}}} \right)\\ &= 59.82\;^\circ {\rm{C}}\end{aligned}\)

Thus, the temperature at the length of 18.70 cm is\(59.82\;^\circ {\rm{C}}\).

From equation (i), the temperature at the length of 14.60 cm can be calculated.

\(\begin{aligned}{c}T\left( {14.60{\rm{ cm}}} \right) &= 0^\circ {\rm{C}} + \left( {14.60{\rm{ cm}} - 12.61{\rm{ cm}}} \right)\left( {9.823\;^\circ {\rm{C/cm}}} \right)\\ &= 1.99{\rm{ cm}} \times \left( {9.823\;^\circ {\rm{C/cm}}} \right)\\ &= 19.55\;^\circ {\rm{C}}\end{aligned}\)

Thus, the temperature at the length of 14.60 cm is\(19.55\;^\circ {\rm{C}}\).