Question

A vessel containing $5{\text{ }}litres$of a gas at $0.8{\text{ }}m$pressure is connected to an evacuated vessel of volume $3{\text{ }}litres$. The resultant pressure inside will be (assuming whole system to be isolated)
A. $\dfrac{4}{3}m$
B. $0.5m$
C. $2.0m$
D. $\dfrac{3}{4}m$

Answer 1

Hint:
In an isolated thermodynamic system, heat transfer and temperature can be assumed as constant, and at a constant temperature, we can apply the Boyles equation which is defined as $PV = constant$ to determine the value of pressure inside an evacuated vessel which helps to identify the correct option for the given problem.

Formula used: An Ideal-Gas Equation, $PV = nRT$
where $P$ stands for pressure, $V$ for volume, $n$ for moles, $R$ for the universal gas constant, and $T$ for temperature.


Complete step by step solution:

It is given that a vessel containing $5{\text{ }}litres$of a gas at $0.8{\text{ }}m$pressure is connected to an evacuated vessel of volume $3{\text{ }}litres$. It means ${V_1} = 5{\text{ }}litres$ and ${P_1} = 0.8{\text{ }}m$.
And as the vessel is connected to an evacuated vessel therefore, ${V_2}{\text{ = 5 + 3 = 8 }}litres$.
Now, the expression for an ideal-gas equation can be stated as: -
$PV = nRT$
In an isolated system let us assume $T = constant$. Therefore,
$ \Rightarrow PV = nR(constant)$
As, $n\,and\,R$ are constant for a given ideal gas.
$ \Rightarrow PV = constant$
$ \Rightarrow {P_1}{V_1} = {P_2}{V_2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(1)$
On substituting the values from the question in equation $(1)$, we get
$ \Rightarrow 0.8 \times 5 = 8 \times {P_2}$
$ \Rightarrow {P_2} = \dfrac{{0.8 \times 5}}{8} = 0.5m$
Thus, the resultant pressure inside a vessel will be $0.5m$.
Hence, (B) is the correct option.





Note:
In this problem, to determine the value of pressure inside a fully isolated system, we have to apply the Boyles equation, i.e., $PV = constant$, and then add the volume of gas with the volume of the evacuated vessel and simplify it, then analyze each given option carefully to give an accurate answer.