Question

The length of a mercury column of a thermometer are 1.06cm &20.86cm respectively at a standard fixed points. What is the temperature of the body which produces 7.0cm of this mercury column

Answer 1

Solution:

Standard fixed points are:

$t_0=0^{\circ} С$

$t_1=100^{\circ} С$

Let's write the linear expansion equation for temperature t₁:

$l_1-l_0=\alpha{l_0}(t_1-t_0)$

From previous equation we can find the coefficient of thermal expansion of mercury:

$\alpha=\frac{l_1-l_0}{l_0(t_1-t_0)}=\frac{20.86-1.06}{1.06\cdot{100}}=0.1868$ K^-1

Let's write the linear expansion equation for temperature t₂:

$l_2-l_0=\alpha{l_0(t_2-t_0)}$

$t_2-t_0=\frac{l_2-l_0}{\alpha{l_0}}=\frac{7.0-1.06}{0.1868\cdot{1.06}}=30^{\circ} С$

$t_2=30^{\circ} С$

Answer:

The temperature of the body is 30^o C.