A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to ( 1 8 )^ th of its initial volume. The ratio of final pressure to initial pressure is

Step-by-step solution

For a sudden compression in a thermally insulated container, the process is adiabatic. The equation for an adiabatic process is P V^ = constant . For a monoatomic gas, = 5 3 . Given V₂ = V₁ 8 . P₂ P₁ = ( V₁ V₂ )^ P₂ P₁ = (8)^ 5 3 = (2^3)^ 5 3 = 2^5 = 32 The ratio of final pressure to initial pressure is 32:1 . Answer: 32:1