Question

At T Kelvin and pressure of P atm, certain gas is present in a vessel. If the vessel is divided into two equal compartments by a partition, the pressure in each compartment is:
A. 4P atm
B. P atm
C. P/4 atm
D. 2P atm

Answer 1

Hint: Solve this question by using ideal gas equation, i.e. PV=nRT. We can easily use this equation to relate pressure (P), volume (V) and number of moles (n). Pressure is inversely proportional to volume.

Complete step by step answer:
According to the question, there is a vessel. Let us assume that its volume is ‘V litre’.
The gas is present at a constant temperature of ‘T Kelvin’ and pressure ‘P atm’.
Now, the vessel is divided into two equal compartments by a partition.
Therefore, the volume becomes ‘V/2 litre’ for both compartments.
From ideal gas law, we can see that volume is indirectly proportional to pressure, i.e. as volume decreases, pressure increases and vice-versa.
We can also relate it by Boyle’s law as – \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\], where,
\[{{P}_{1}}\]= Pressure at condition 1 = P atm
\[{{V}_{1}}\]= Volume at condition 1 = V litre
\[{{P}_{2}}\]= Pressure at condition 2 = x
\[{{V}_{2}}\]= Volume at condition 2 = V/2
Now, let us substitute the values.
Therefore, P V = X (V/2)
X = 2P.
Therefore, the answer is – option (d) – the pressure in each compartment is 2P.

Additional Information:
“The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under many conditions, although it has several limitations.” Mathematically, it is expressed as –
PV= nRT, where,
P = Pressure
V = Volume
N = moles
R = Universal Gas Constant
T = Temperature

Note: “Boyle's law, also referred to as the Boyle–Mariotte law, or Mariotte's law, is an experimental gas law that describes how the pressure of a gas tends to increase as the volume of the container decreases.”