A cylindrical Container contains a light (so that you can neglect its weight), a

Question

A cylindrical Container contains a light (so that you can neglect its weight), airtight piston that can move up and down the inside of the cylinder. The radius of the piston is 10 cm. The temperature the air in the piston is 20 degree C. When the system of the piston, cylinder anti air inside the cylinder as r equilibrium, the piston is 15 cm above the base of the cylinder. (a) How many moles of gas are in the cylinder? (b) The temperature of the air inside the cylinder is raised by 100 degree C. What is the height of the piston above the base of the cylinder? (c) A heavy block is placed on the piston which causes the piston to move back to its original height, What is the pressure inside the cylinder? (The temperature remains the same as for part b). (d) What is the mass of the block placed on the piston?

Explanation / Answer

(a)

Volume of gas, V = pi*102*15 = 4712.38 cm3 = 4.712 L

T = 293 K

P = 1 atm

Putting values in the equation and solving:

PV = nRT

n = PV/RT = (1*4.712)/(0.0821*293) = 0.196 moles

(b)

T2 = 393 K

Since P remains constant here, so

V1/T1 = V2/T2

Putting values we get:

V2 = (4.712/293)*393 = 6.32 L = 6320 cm3

So, height h2 = 6320/(pi*102) = 20.12 cm

(c)

Since T remains constant here, so

P2*V2 = P3*V3

Putting values we get:

P3 = (1*20.12)/4.712 = 4.27 atm

(d)

P3 = 4.27 atm = 432657.7 N/m2.

P = (mg)/A

So, m = (P*A)/g = ( 432657.7*pi*(0.1)2 )/9.81 = 1385.56 kg

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