Note on Calibration of Thermometer, Zeroth Law and Construction of Mercury Thermometer

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Calibration of thermometer

Lower fixed point (LFP): It is the temperature at which pure ice melts at standard pressure 760 mm Hg.

Upper fixed point (UFP): It is the temperature at which pure water boils at standard pressure.

Different temperature scales are:

  1. Celsius scale
  2. Kelvin scale
  3. Fahrenheit scale
  4. Reumer scale
Comparison of different temperature scale
Comparison of different temperature scale

Celsius scale

In this case, the lower fixed point is zero-degree celsius and an upper fixed point is 100. The parts of LFP and UFP is divided into 100 equal parts each part representing 10C.

Kelvin scale

In this case, the LFP is taken as 273 K and UFP is taken as 373 K. The space between Kelvin scale is derived into 100 parts each represents 1K.

Fahrenheit scale

In this case, the lower fixed point is 32oF and upper fixed point is 212oF. The space between LFP and UFP is divided into 180 parts each part represents 10F.

Reumer scale

In this case, the lower fixed point is zero-degree reumer and an upper fixed point is 80-degree reumer. The space between reumer scales divided into 80 parts each part 1 reumer.

Relation between Different Temperature Scales

There are two temperature scales but different divisions between them. If C, F, R and K be the temperature of a body in Celcius, Fahrenheit, reumer and Kelvin scale respectively then we have,

$$\frac{C-0}{100-0} =\frac{F-32}{212-32} = \frac{R-0}{80-0} = \frac{K-273}{373-273} $$

$$or, \frac{C}{100} =\frac{F-32}{180} = \frac{R-0}{80} = \frac{K-273}{100} $$

$$or, \frac{C}{5} =\frac{F-32}{9} = \frac{R}{4} = \frac{K-273}{5} $$

The conversion between the temperatures in absolute scale, T and celsius scale is

T = C + 273.15

So, ice point, T = 0+ 273.15 = 273.15 K

And boiling point T = 100+ 273.15 = 373.15 K

These points are written approximately as 273 K and 373 K. The absolute zero temperature is equal to 0 K i.e.

0 K = C + 273

or C = -2730C.

Three objects in thermal equilibrium
Three objects in thermal equilibrium

Thermal Equilibrium and Zeroth Law of Thermodynamics

The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

According to the zeroth law, “Two systems are said to be in thermal equilibrium if they have the same temperature." When heat substance is kept in contact with the cold substance. Heat will be transferred from hotter substance to colder substance and both substances will attain the same temperature. The bodies are then said to be in thermal equilibrium.

Consider two systems A and B separated to each other by an insulating wall but each being in contact with third system C through the conducting wire as in the figure. After sometimes, the system A will be in thermal equilibrium with system C and similarly system B will be in thermal equilibrium with system C. If insulating wire is changed by conducting wire, experiments show that no further change in temperature takes place in the systems A and B indicating that the system A was in thermal equilibrium with system B. This experiment shows the zeroth law of thermodynamics.

Construction of a Mercury Thermometer

Construction of a mercury Thermometer
Construction of a Mercury Thermometer

To construction a mercury thermometer, a clean fine glass capillary tube having a bulb at one end is taken as shown in the figure. The bulb is filled with pure and dry mercury with the help of funnel by alternate heating and cooling. The bulb is placed in a bath whose temperature is higher than the maximum temperature to be measured with the thermometer. The open end tube of the capillary tube is sealed after the air is completely exhausted out from the bulb and capillary tube. The tube filled with mercury is kept for several days for cooling before marking fixed points. Two fixed points of temperature are chosen before graduating the thermometer.

To mark the lower fixed point, the bulb of the thermometer is kept well inside the melting ice as shown in the figure. After some time, the mercury level falls and becomes constant at a certain point. The level is marked on the glass which represents the lower fixed point of the thermometer.

To mark the upper fixed point, the thermometer is placed in a hypsometer containing water as shown in the figure. The bulb of the thermometer should be outside the water. When the mercury level becomes stationary at a temperature of steam, the level is marked, which represents the upper fixed point of the thermometer. The thermometer is graduated in 100 equal divisions between these points.

Reference

https://en.wikipedia.org

  1. Lower fixed point is the temperature at which pure ice melts at standard pressure 760 mm Hg.
  2. In celsius scale, the lower fixed point is zero-degree celsius and an upper fixed point is 100.
  3. In kelvin scale, the LFP is taken as 273 K and UFP is taken as 373 K. 
  4. In fahrenheit scale, the lower fixed point is 32 o Fand upper fixed point is 212o F. 
  5. In reumer scale, the lower fixed point is 0 o reumer and upper fixed point is 80o reumer. 
  6. Upper fixed point is the temperature at which pure water boils at standard pressure.
  7. The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.
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