As shown in the figure, a sealed cylinder of ideal gas is divided into two parts
ID: 1473265 • Letter: A
Question
As shown in the figure, a sealed cylinder of ideal gas is divided into two parts by a piston that can move up and down without friction. There is ideal gas in both parts, but the gas from one part is isolated from that in the other part by the piston. The volume occupied by the gas in the lower part is twice that occupied by the gas in the upper part, while the temperature is the same in both parts. The pressure in the upper part is 6400 Pa, and the weight of the piston is 80.0 N. The piston is in its equilibrium position. The cross-sectional area of the cylinder is 100 cm2.
Determine:
(a) the pressure in the lower part.
__Pa
(b) the ratio of the number of moles of gas in the lower part to the number of moles in the upper part.
Please show all work!
Explanation / Answer
A) pressure in the lower part is P2 = F/A = 80/(100*10^-4) = 8000 Pa
B) Since the temparature is same in two parts
no.of moles n = (P*V)/(R*T)
Temparature is T = (P*V)/(R*n)
P1*V1/n1 = P2*V2/n2
n2/n1 = (P2*V2)/(P1*V1)
given that V2 = 2*V1 = (8000*2*V1)/(6400*V1) = 2.5
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