
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
161.4k+ views
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.
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.
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