Question

Volume of a cylinder containing $10$ marbles and gas is $1$ litre at $2$ atm pressure. Now pressure on the cylinder is increased to $4$ atm, at which volume becomes $725$ ml. Calculate volume of each marble.

• A. $60ml$
• B. $45ml$
• C. $57ml$
• D. $39ml$

Answer 1

The correct option is B $45ml$

Let us assume that the volume of each marble be $v$ ml. Let the gas behave as an ideal gas. Assume that the compression is done as an isothermal process.

$P_1=2atm$

Initial volume of the gas $=V_1=1000-10v$ ml

$P_2=4atm$

$V_2=725-10v$ ml

Using Gas equation: $P_1{V}_1=P_2{V}_2$

$⟹2(100-10v)=4(725-10v)$

$⟹20v=900$

$⟹v=45$ ml