Answer to Question #172586 in Molecular Physics | Thermodynamics for Bahaa

Question

The length of the mercury column in a mercury-in-glass thermometer is 

5 cm when the bulb is immersed in water at its triple point. What is the 

temperature on the mercury-in-glass scale when the length of the col￾umn is 6.0 cm? What will the length of the column be when the bulb is 

immersed in a liquid at 100° above the ice point, as measured on the mer￾cury-in-glass scale? If the length of the column can be measured to within 

only 0.01 cm, can this thermometer be used to distinguish between the 

ice point and the triple point of water? You may take the temperature of 

the ice point, as measured on the mercury-in-glass scale, as 273.15 K.

Answer 1

a. Temperature at triple point of water = 273.16 K

length of mercury (x) = 5.0cm

Temperature at 6.0cm = ?

$\theta = \dfrac{273.16}{5.0} × 6.0 = 327.79K$

b. Temperature at steam point = 373.15 K

$l = \dfrac{5.0}{273.16}× 373.15 = 6.83\ cm$

c. ∆x = 0.1cm

$∆ \theta = \dfrac{273.16}{50} × 0.01 = 0.55K$

But the difference between the ice point of water and the triple point of water is 0.01 K.

Therefore, the length of the column cannot distinguish between the ice point and the triple point of water.