Physics help? In Exploration 14.4, we analyzed a cylinder filled with ideal gas
ID: 1471636 • Letter: P
Question
Physics help?
In Exploration 14.4, we analyzed a cylinder filled with ideal gas that is sealed by a piston that is above the gas. The piston is a cylindrical object, with a weight of 20.0 N, that can slide up or down in the cylinder without friction. The inner radius of the cylinder, and the radius of the piston, is 10.0 cm. With the top of the piston exposed to the atmosphere, at a pressure of 101.3 kPa, we determined the pressure inside the cylinder. Now, very slowly, so that the gas inside the cylinder stays constant at the temperature of its surroundings, sand is poured onto the top of the piston. When 210. N of sand has been added to the piston, determine: (a) the gauge pressure inside the cylinder (b) the ratio of the final volume occupied by the gas after the sand is added to the volume occupied by the gas before the sand is added.
Explanation / Answer
area of the piston, A = pi*r^2
= pi*0.1^2
= 0.0314 m^2
a) Guage pressure inside the cyllinder, P_gauge = (w_piston + W_sand)/A
= (20 + 210)/0.0314
= 7325 pa <<<<<<<<<<-------------Answer
b) before sand poured, inside pressure,
P1 = 101.3*10^3 + W-piston/A
= 101.3*10^3 + 20/0.0314
= 101.937*10^3 pa
after sand poured, inside pressure,
P2 = 101.3*10^3 + (W-piston + W_sand)/A
= 101.3*10^3 + 7325
= 108.625*10^3 pa
At constant temeratute, P*V = constant
so,
V2/V1 = P1/P2
= 101.937*10^3/(108.625*10^3)
= 0.9384 <<<<<<<<<<-------------Answer