Question

A cylinder of 5 L capacity, filled with air at NTP is connected with another evacuated cylinder of 30 L capacity. The resultant air pressure in both the cylinder will be:
A) $10.8$ cm of Hg
B) $14.9$ cm of Hg
C) $21.8$ cm of Hg
D) $38.8$ cm of Hg

Answer 1

Hint: We know that the product of pressure and volume of a fixed amount of a gas remains constant at a constant temperature. So, the pressure and volume of the cylinder will be equal to resultant pressure and volume. Use the formula to find the value of resultant pressure.
Formula used:
 \[{\text{PV = constant}}\]
Here, \[{\text{P}}\]= pressure of the gas
\[{\text{V}}\]= volume of the gas

Complete step by step answer:
Let us consider the cylinder with 5 L capacity as cylinder 1.
We can write the formula for cylinder 1 as:
\[\;{{\text{P}}_{\text{1}}}{{\text{V}}_{\text{1}}}{\text{ = constant}}\] ……(equation 1)
Here, \[{{\text{P}}_{\text{1}}}\] = Pressure at NTP
                 = 76 cm of Hg
\[{{\text{V}}_{\text{1}}}\] = Volume of cylinder
       = 5 L
Now, let us consider the resultant cylinder (i.e. cylinder of 5 L capacity connected with the cylinder of 30 L capacity) as cylinder 2.
So, we can write the formula for cylinder 2 as:
\[\;{{\text{P}}_2}{{\text{V}}_2}{\text{ = constant}}\] …… (equation 2)
Here, \[{{\text{P}}_{\text{2}}}\] = Pressure of resultant air in both the cylinder
\[{{\text{V}}_{\text{2}}}\] = Volume of resultant cylinder
Hence,
 $
  {{\text{V}}_{\text{2}}} = 5 + 30 \\
   = 35{\text{ L}} \\
 $
Comparing equation 1 and equation 2 we get:
\[{P_1}{V_1} = {P_2}{V_2}\]
Let us substitute the respective value we get:
\[{\text{76 (cm of Hg)} \times 5 (L) = }{{\text{P}}_{\text{2}}}{\text{} \times 35 (L)}\]
By rearranging the equation we get:
\[\dfrac{{{\text{76 (cm of Hg)} \times {5 (L)}}}}{{{\text{35 (L)}}}}{\text{ = }}{{\text{P}}_{\text{2}}}\]
As volume terms are present in numerator and denominator, we should cancel the term to get:
\[\dfrac{{{\text{76 (cm of Hg)} \times 1 ({L})}}}{{{\text{7} ({L})}}}{\text{ = }}{{\text{P}}_{\text{2}}}\]
Now, by dividing the pressure value by 7 we get:
\[{{\text{P}}_{\text{2}}}{\text{ = 10}}{\text{.8 cm of Hg}}\]

Therefore, we can conclude that the correct answer to this question is option A.

Note:
We can get confused between the selection of \[{{\text{P}}_{\text{2}}}\] as the pressure of a cylinder having 30 L capacity or the resultant pressure of cylinder 1 plus cylinder 2. As cylinder 2 having 30 L is evacuated, the pressure inside it is zero and thus, we choose \[{{\text{P}}_{\text{2}}}\] as resultant pressure.