Question

A standard mercury thermometer consists of a hollow glass cylinder, the stem, attached to a bulb filled with mercury. As the temperature of the thermometer changes, the mercury expands (or contracts) and the height of the mercury column in the stem changes. Marks are made on the stem to denote the height of the mercury column at different temperatures such as the freezing point (0∘C ) and the boiling point (100∘C ) of water. Other temperature markings are interpolated between these two points. Due to concerns about the toxic properties of mercury,many thermometers are made with other liquids. Consider drainingthe mercury from the above thermometer and replacing it withanother, such as alcohol. Alcohol has a coefficient of volumeexpansion 5.6 times greater than that of mercury. The amount ofalcohol is adjusted such that when placed in ice water, thethermometer accurately records 0 C. No other changes are made tothe thermometer.

Required:
a. When the alcohol thermometer is placed in 22 C water,what temperature will the thermometer record?
b. When the alcohol thermometer is placed in a -12 Csubstance, what temperature will the thermometer record?

c. If you want to design a thermometer with the same spacingbetween temperature markings as a mercury thermometer, how must thediameter of the inner hollow cylinder of the stem of the alcoholthermometer compare to that of the mercury thermometer? Assume thatthe bulb has a much larger volume than the stem.

1. 5.6 times wider
2. √5.6 times wider
3. the same diameter but different bulbsize
4. √5.6 times smaller
5. 5.6 times smaller

Answer 1

Answer:

a)  T_alcohol = 123.2ºC , b) T_alcohol = -67.2ºC  and c)  r_alcohol =√5,6 r_mercury  

Explanation:

We can solve this problem using the thermal expansion equation

            ΔV = β Vo ΔT

indicates that alcohol has a coefficient of expansion 5 times that of mercury

           β_alcohol = 5 β_mercury

the amount of alcohol used from a correct reading at zero degrees, let's substitute in the equation for alcohol

           ΔV = β_ alcohol ΔT

           ΔV = 5.6 β_mercury ΔT

we see that the expansion is 5 times the expansion of mercury

           T_alcohol = 5.6 T_mercury

           T_alcohol = 5.6 22

           T_alcohol = 123.2ºC

b) in the case of T = -12ºC

          T_alcohol = 5.6 (-12)

          T_alcohol = -67.2ºC

c) In this case we want the division to give the same value for the two thermometers

let's use the volume ratio

          V = A L

where A is the area of ​​the circle and L the length that the alcohol travels

We know that the volume of alcohol is 5.6 times the volume of mercury

        V_alcohol = 5.6 V_mercury

        A_alcohol V = 5.6 A_mercury L

        A_alcohol = 5.6 A_mercury

if the area of ​​a plum is A = π r², when substituting in this equation

         π r_alcohol² = 5.6 π r_mercury²

           r_alcohol =√5,6 r_mercury

the consequence the radius of the alcohol thermometer must be √5.6 times the radius of the Mercury thermometer; the correct answer is 2