Correct Answer - Option 1 : -2731.5
Concept:
Absolute zero temperature: The temperature at which the enthalpy and entropy of a gas reach their minimum value taken as zero. All the particles stop moving and all the disorders disappear.
The value of absolute zero temperature is 0K or -273.15°C
Celsius scale: Celsius sale also called centigrade scale is based on 0°C for the freezing point of water and 100°C for boiling pint for water.
Methods of temperature measurement:
1)Two reference point system:
In this method, two reference points are used
- Ice point (0°C) = Ti
- Steam point (100°C) = Ts
In this we consider the basic equation T = a + b × X
\({\bf{T}}\; = \;\frac{{ - 100 × {{\bf{X}}_{\bf{i}}}}}{{{{\bf{X}}_{\bf{s}}} - {{\bf{X}}_{\bf{i}}}}} + \;\frac{{100}}{{{{\bf{X}}_{\bf{s}}} - {{\bf{X}}_{\bf{i}}}}} × {\bf{X}}\)
where, Xi = ice point in new temperature scale, Xs = steam point in new temperature scale, X = required temperature on the new temperature scale corresponding to the given standard temperature scale
2) Single reference point system:
In this method single reference points used i.e triple point of water (273.15K)
Here we consider the basic equation T = a × X
\({\bf{T}} = 273.15 \times \;\frac{{\bf{X}}}{{{{\bf{X}}_{{\bf{tp}}}}}}\)
where, X = required temperature on the new temperature scale, Xtp = triple point temperature on the new temperature scale, T = given standard temperature
Calculation:
Given:
The freezing point of water (Xi) = 0°X and boiling point of water (Xs) = 1000°X in an unknown temperature scale
The freezing point of water (Ti) = 0°C and boiling point of water (Xs) = 100°C on the Celsius scale
we know the basic equation for two reference point system
T = a + b × X .......(A)
Ti = a + b × Xi .......(1)
Ts = a + b × Xs .......(2)
substituting the above values in equation 1 and 2
0 = a + b × 0
100 = a + b × 1000
We get a = 0 and b = 0.1, then substituting absolute zero temperature (T) = -273.15 and values of a and b in equation A
T = a + b × X
-273.15 = 0 + 0.1 × X
∴ X = -2731.5°X
If two thermometers are agreed at ice point and steam point it does not mean that the intermediate temperature is also the same and all scales are arbitrary