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Mechanical Properties Of Fluids

Question
CBSEENPH11019535

The resistance of platinum wire resistance thermometer at ice point is 5.5Ω and 7.5Ω at steam point. The pressure exerted by gas in constant volume gas thermometer at respective points is 100cm and 136cm of mercury. When both the thermometers are put in a bath, the resistance of platinum resistance thermometer is 7.1Ω and the pressure of the gas is 128cm of mercury. Compare the temperature recorded by two thermometers. 

Solution
Resistance thermometer: 
We have,
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Let t be the temperature of bath recorded by resistance thermometer. 
∴                straight t subscript 1 space equals space fraction numerator straight R subscript bath minus space straight R subscript straight o over denominator straight R subscript 100 minus straight R subscript straight o end fraction cross times 100
                  space space space space equals fraction numerator 7.1 minus 5.5 over denominator 7.5 minus 5.5 end fraction cross times 100
space space space space equals space 80 degree straight C 
Gas Thermometer: 
We have,
straight P subscript straight o space equals space 100 cm space of space Hg
 
space space straight P subscript 100 space equals space 136 cm space of space Hg 
straight P subscript bath space equals 128 space cm space of space Hg
Let t2 be the temperature of bath recorded by gas thermometer. 
∴           straight t subscript 2 equals fraction numerator straight P subscript straight theta minus straight P subscript straight o over denominator straight P subscript 100 minus straight P subscript straight o end fraction cross times 100 

               equals fraction numerator 128.5 minus 100 over denominator 136 minus 100 end fraction cross times 100
equals space 79.17 degree straight C 
The temperature of bath on platinum scale is 80°C and that of same bath on gas scale is 79.17°C.