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Question

The ideal gas law, which relates the P, V and temperature T of an ideal gas in a closed box, given as PV = nRT, can be manipulated to construct an effective thermometer. A "constant volume gas thermometer” uses a sample of gas (commonly, nitrogen or helium) in a closed chamber, thus fixing the volume V. The temperature is then measured by reading off the corresponding pressure P. At the freezing point of water, it is seen that a gas thermometer records a pressure of 0.9 x 105 Pa; it also records a pressure of 1.2 x 105 Pa at the boiling point of water. What pressure will you find in the gas chamber at a room temperature of 230C?


A

0.81 x 105 Pa

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B

1.34 x 105 Pa

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C

0.64 x 105 Pa

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D

0.97 x 105 Pa.

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Solution

The correct option is D

0.97 x 105 Pa.


For an ideal gas at constant V,

P ∝ T

(for some proportionality constant 'C').

Let (TF, PF) and (TB,PB) be the (T,P) values for the freezing and the boiling points of water respectively. We can write -

(1)

Subtracting,

(2)

From relation (1) and (2), we can write -

(3)

Comparing (2) and (3),


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