Question

Two ideal gas thermometers Aand Buse oxygen and hydrogen respectively. The following observations are made:

Temperature Pressure thermometer A Pressure thermometer B
Triple-point of water 1.250 × 10⁵ Pa 0.200 × 10⁵ Pa
Normal melting point of sulphur 1.797 × 10⁵ Pa 0.287 × 10⁵ Pa

(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers Aand B?

(b) What do you think is the reason behind the slight difference in answers of thermometers Aand B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?

Solution

(a)
Triple point of water, T = 273.16 K

At this temperature, pressure in thermometer A, P_A = 1.250 × 10⁵ Pa
Let T₁ be the normal melting point of sulphur.
At this temperature, pressure in thermometer A, P₁ = 1.797 × 10⁵ Pa
According to Charles’ law, we have the relation,

fraction numerator straight P subscript straight A over denominator space straight T space end fraction space equals space begin inline style fraction numerator space straight P subscript 1 over denominator space straight T subscript 1 end fraction end style space therefore space straight T subscript 1 space equals space fraction numerator space straight P subscript 1 straight T over denominator straight P subscript straight A end fraction space space space space space space space space space equals space fraction numerator 1.797 space cross times space 10 space cross times space 273.16 over denominator left parenthesis 1.250 space cross times space 10 to the power of 5 right parenthesis end fraction space space space space space space space space space equals space 392.69 space straight K space Therefore comma space the space absolute space temperature space of space the space normal melting space point space of space sulphur space as space read space by space thermometer space straight A space is space 392.69 space straight K. At space triple space point space 273.16 space straight K comma space the space pressure space in space thermometer space straight B comma space straight P subscript straight B space equals space 0.200 space cross times space 10 to the power of 5 space Pa At space temperature space straight T subscript 1 comma space pressure space in space thermometer space straight B comma space straight P subscript 2 space equals space 0.287 space cross times space 10 to the power of 5 space Pa space According space to space Charle apostrophe straight s space Law comma space we space can space write space the space relation comma space straight P subscript straight B over straight T space equals space straight P subscript 1 over straight T subscript 1 space fraction numerator left parenthesis 0.200 space cross times space 10 to the power of 5 right parenthesis over denominator 273.16 end fraction space equals space fraction numerator space left parenthesis 0.287 space cross times space 10 to the power of 5 right parenthesis over denominator straight T subscript 1 end fraction therefore space straight T subscript 1 space equals space open square brackets fraction numerator left parenthesis 0.287 space cross times 10 to the power of 5 right parenthesis over denominator 0.200 cross times 10 to the power of 5 end fraction close square brackets cross times 273.16 space space space space space space space space space space space equals space 391. space 98 space straight K space Therefore comma space the space absolute space temperature space of space the space normal space melting space point space of space sulphur space as space read space by space thermometer space straight B space is space 391.98 space straight K.

b) The oxygen and hydrogen gas present in thermometers A and B respectively are not perfect ideal gases. Hence, there is a slight difference between the readings of thermometers A and B.
To reduce the discrepancy between the two readings, the experiment should be carried under low pressure conditions. At low pressure, these gases behave as perfect ideal gases.

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Temperature	Pressure thermometer A	Pressure thermometer B
Triple-point of water	1.250 × 10⁵ Pa	0.200 × 10⁵ Pa
Normal melting point of sulphur	1.797 × 10⁵ Pa	0.287 × 10⁵ Pa