A cylinder containing ideal gas is sealed by a piston that is above the gas. The

Question

A cylinder containing ideal gas is sealed by a piston that is above the gas. The piston is a cylindrical object, with a weight of 30.0 N, which can slide up or down in the cylinder without friction. The inner radius of the cylinder, and the radius of the piston, is 9.00 cm. The top of the piston is exposed to the atmosphere, and the atmospheric pressure is 101.3 kPa. The cylinder has a height of 30.0 cm, and, when the temperature of the gas is 20°C, the bottom of the piston is 14.0 cm above the bottom of the cylinder.

a).  Determine the pressure of the gas in the cylinder. Give your answer in kilo-pascal (kPa).

b). Find the number of moles of ideal gas in the cylinder.

c).  Heat is added, gradually raising the temperature of the gas to 195°C. Calculate the distance between the bottom of the cylinder and the bottom of the piston when the piston comes to its new equilibrium position. Please give your answer in centimeters (cm).

Explanation / Answer

a)

calculate the number of moles of ideal gas in cylinder

P = Patm + Fnet / A

P = 101325 pa + 30 / (pi x 0.09^2)

P = 102504 pa

P = 102.504 kpa

b)

calculate the number of moles of ideal gas in the cylinder

PV = nRT

n = PV / RT

n = (102504 x pi x 0.09^2 x 0.30) / (8.314 x 293)

n = 0.32 moles

c)

Required distance is

PV' = nRT'

102504 x pi x 0.09^2 x h' = 0.32 x 8.314 x (195 + 273)

h' = 0.4773 m = 47.73 cm

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