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?
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?
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),
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),
