A cylinder filled with ideal gas is sealed by a piston that is above the gas. Th
ID: 1509666 • Letter: A
Question
A cylinder filled with ideal gas is sealed by a piston that is above the gas. The piston is a cylindrical object, with a weight of 40.0 N, that can slide up or down in the cylinder without friction. The area of the top (or the bottom) of the piston is 100 cm2. The top of the piston is exposed to the atmosphere, and the atmospheric pressure is 100 kPa. As shown in the figure, the piston is tied to a string that passes over a pulley system and is tied to a block that has a weight of 90.0 N. Both the block and the piston are in equilibrium. The cylinder has a height of 50.0 cm, and, when the temperature of the gas is 20°C, the bottom of the piston is 25.0 cm above the bottom of the cylinder.
a) Find the pressure in the cylinder.
b) Find the number of moles of ideal gas in the cylinder.
Explanation / Answer
a)
from the force balance
Tansion in string = 90 because block is at rest
tansion in string + PA = 40 + P0*A because piston is at rest
where P is the pressure of gas exerted upword on piston
P0 is the atmospheric pressure exerted on piston downword
90 + PA = 40 + P0*A
P* 100*10^(-4) = 40 - 90 + 10^5 * 100*10^(-4) = 950
P = 95000 Pa = 0.95 atm
b)
T = 20 C = 20 + 273.15 = 293.15 K
V = A*h = 100*10^(-4) * 0.25 = 2.5*10^(-3) m^3
P = 0.95 atm = 95000 Pa
from the ideal gas equation
PV=nRT
95000 * 2.5*10^(-3) = n * 8.314 * 293.15
n = 0.097 mole
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