A 6.0-cm-diameter cylinder of nitrogen gas has a 4.0-cm-thick movable copper pis

Question

A 6.0-cm-diameter cylinder of nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented vertically, as shown in the figure, and the air above the piston is evacuated. When the gas temperature is 20 degrees C, the piston floats 20 cm above the bottom of the cylinder.

a) What is the gas pressure?
b)How many gas molecules are in the cylinder?
c)Then 2.0 J of heat energy are transferred to the gas. What is the new equilibrium temperature of the gas?
d)What is the final height of the piston?
e)How much work is done on the gas as the piston rises?

Explanation / Answer

(a)

Mass of piston = ?V=??r2h
Pressure = Mg/A = ??r2hg/?r2=?hg

g = 9.80 m/sec^2
?=8.96g/cm3=8.96x10?3kg/10?6m3=8.96x103kg/m3

Pressure = 8960 x .04 (9.80) = 3512 N/m^2 = 3512 Pa. = 3.512 kpa

In significant figures, this would be 3.5 kpa

(b)

I think your question is what is the work done by the gas in moving piston to 6cm (from 20cm to 26 cm )

i small advice for u ..pls don't use terms like float, rise and final height, its confusing...

Work done = Force * displacement
6cm = 0.06 m
force=3500 / 0.002827 = 1237871.78 N

workdone = 1237871.78 * 0.06 = 74272.3 Nm

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