An ideal gas is confined in a long cylindrical vessel equipped with a frictionless piston that has a weight of 1 kg and a cross-sectional area of 10 cm ^2 , as shown in the figure. The vessel is placed inside a large chamber holding air at an atmospheric pressure of 100 kPa . The initial length of the gas column is 20 cm . Determine the final length of the gas column if the chamber is subsequently completely evacuate

Step-by-step solution

Let the initial pressure of the gas inside the cylinder be P₁ . P₁ = P₀ + mg A Given P₀ = 100 kPa , m = 1 kg , and A = 10 cm ^2 = 10⁻³ m ^2 . Taking g = 10 m/s ^2 , the pressure exerted by the piston is: mg A = 1 10 10⁻³ = 10^4 Pa = 10 kPa Therefore, P₁ = 100 kPa + 10 kPa = 110 kPa . The initial volume of the gas is V₁ = A L₁ , where L₁ = 20 cm = 0.2 m . When the chamber is completely evacuated, the external pressure becomes zero. The final pressure of the gas is P₂ = 0 + mg A = 10 kPa . Let the final length of the