Question

A container of $5l$ has a gas pressure of $0.8m$column of Hg. This is joined to an evacuated container of $3l$capacity. The resulting pressure will be: (at constant temperature$T$)

& A.\dfrac{4}{3}m \\\ & B.0.5m \\\ & C.2.0m \\\ & D.\dfrac{3}{4}m \\\ \end{aligned}$$

Answer 1

Ideal gas law or the general gas equation is the combination of Boyle’s Law, Charles’s law, Avogadro’s law and Gay Lussac’s law. It gives the relationship between the pressure $P$ applied on a $V$ volume of the gas which contains $n$ number of molecules at temperature $T$.

Formula used:
$PV=nRT$

Complete step-by-step answer:
Let us assume that the gas in the container is ideal and contains $n$ number of molecules. Here since the temperature is constant, we can say that the system is undergoing an isothermal process.
Given that the initially the pressure in the gas is $P_{1}=0.8m$ and the volume is $V_{1}=5l$ and since the container of capacity $5l$ is connected to another whose maximum capacity is$3l$ , then we can say that the new volume $V_{2}=3+5=8l$, let the $P_{2}$ be the final pressure .
Then, from ideal gas law we now that $PV=nRT$
Clearly, $n$, $R$, $T$ are constant here.
Then, we get $PV=constant$
$\implies P_{1}V_{1}=P_{2}V_{2}$
Substituting the values we get $0.8\times 5=P_{2}\times 8$
$\implies P_{2}=\dfrac{ 0.8\times 5}{8}=0.5m$
Hence the answer is option $B.0.5m$

So, the correct answer is “Option B”.

Additional Information: However, the ideal gas law doesn’t give any information of the nature of reaction, i.e. when the gas is expanding or compressing does it absorb heat or release heat. Also as the name suggests these gases are ideal and such gases don't exist in the real world they are hypothetical in nature.

Note: From ideal gas law, we know that $PV=nRT$ where $P$ is the pressure applied on the and $V$ is the volume of the gas which contains $n$ number of molecules at temperature $T$ and $R$ is the gas constant. We can vary the different parameters to understand the behaviours of the gas in various conditions.