Question

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

Answer 1

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.

P1 = 2 atm
Initial volume of the gas = V1 = 1000 - 10 v   ml

P2 = 4 atm
V2 = 725 - 10 v   ml

Using Gas equation:    P1 V1 = P2 V2
=>  2 (100 - 10v) = 4 (725 - 10v)
=> 20 v = 900
=> v = 45 ml
answer.