A piston-fitted cylinder with a 6 cm inner diameter contains 1.4g of Nitrogen (N

Question

A piston-fitted cylinder with a 6 cm inner diameter contains 1.4g of Nitrogen (N2). The mass of the piston is 4.5 kg, and a 20 kg weight rests on the piston. The gas temperature is 30 deg C, and the pressure outside the cylinder is 1 atm.
Prove that the absolute pressure of the gas in the cylinder is 1.86 x 10^5 Pa. Then calculate the volume occupied by the gas, assuming ideal gas behavior. A piston-fitted cylinder with a 6 cm inner diameter contains 1.4g of Nitrogen (N2). The mass of the piston is 4.5 kg, and a 20 kg weight rests on the piston. The gas temperature is 30 deg C, and the pressure outside the cylinder is 1 atm.
Prove that the absolute pressure of the gas in the cylinder is 1.86 x 10^5 Pa. Then calculate the volume occupied by the gas, assuming ideal gas behavior.

Explanation / Answer

d = 6 cm, m = 1.4 g, M = 14 g/mol, m1 = 4.5 kg, m2 = 20 kg T = 273 + 30 = 293 K, P0 = 1 atm = 1.013*10^5 Pa area A = pi*(d/2)^2 = 2.827*10^-3 m^3 pressure P = P0 + (m1 + m2)*g/A = 1.86 x 10^5 Pa. PV = mRT/M so V = mRT/(MP) = 1.31*10^-3 m^3

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