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A constant pressure gas thermometer has a volume of 200cc, 273.2cc and 525.1cc at $0^{o} C$ , $100^{o} C$ and boiling point of sulphur respectively. The resistance possessed by a platinum wire at the same temperature as above $2.00 Ω, 2.778 Ω$ respectively boiling point on the basis of two sets of observations is by gas thermometer is ${(440.1 + x)}^{o} C$ and by resistance thermometer is ${(420.6 + y)}^{o} C$ , then the value of x and y is

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$3^{o} c$

$2^{o} c$

$4^{o} c$

$1^{o} c$

answer is B.

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Detailed Solution

Gas thermometer

$T_{1} = (\frac{V_{T} - V_{0}}{V_{100} - V_{0}}) 100$

$T_{1} = {441.1}^{o} C$

Resistance thermometer

$T_{2} = (\frac{R_{1} - R_{0}}{R_{100} - R_{0}}) 100$

$= {421.6}^{o} C$

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