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Mechanical Properties Of Fluids

Question
CBSEENPH11019529

When a bulb of constant volume air thermometer is placed in melting ice and boiling water at normal pressure, the pressure is found to be 70 cm and 100 cm of mercury respectively. What will be the temperature of the bath, pressure of the gas being 120 cm of Hg?

Solution

We have,
Pressure space when space thermometer space is space placed space in space melting space ice comma space straight P subscript straight o equals space 70 space cm space of space Hg space

Pressure space when space placed space in space boiling space water comma space straight P subscript 100 space equals space 100 space cm space of space Hg space

Pressure space of space the space gas comma space straight P subscript straight theta space equals space 120 space cm space of space Hg 
where. 
straight P subscript straight theta is the pressure of bath whose temperature is to be measured.
We know,  
    straight theta 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 120 minus 70 over denominator 100 minus 70 end fraction cross times 100 space equals space 50 over 30 cross times 100
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#6 {main}</pre>, is the temperature of the bath when pressure is 120 cm of Hg.