An ideal gas is enclosed in a cylinder that has a piston of 100 kg mass and an a

Question

An ideal gas is enclosed in a cylinder that has a piston of 100 kg mass and an area of 7.50 m2 inside the cylinder. The piston is free to move in the cylinder (no friction) maintaining constant gas pressure. The piston – cylinder assembly is located in an environment of zero gage pressure (In other words, ignore atmospheric pressure in your calculations.)

a) How much work is done by the gas if 0.5 moles of the ideal gas is raised from 1500 C to 1800 C? Note, work done by a constant force: is the magnitude of the force times the magnitude of the displacement times the cosine of the angle between them.

b) If the piston were locked in the initial position as described above, what would be the final pressure of the 0.5 gas as it’s temperature is raised from 1500 C to 1800 C?

c) Neatly draw the thermodynamic processes described in parts a) & b) above on a P-V diagram.

Explanation / Answer

Mass = 100 kg => Force = mg = 981 N

Area = 7.5 m^2

Hence pressure = F/A = 981/7.5 = 130.8 N/m^2

Here the pressure is kept constant hence the work done will be P delta V which is nothing but nR delta_T

a) W = 0.5*8.314*300 = 1247.1 J

b) If it is locked then the volume becomes constant hence the pressure is proportional to the temperature.

So P2 = 130.8*1800/1500 = 156.96 N/m^2

c) in the PV diagram, in case of a it will be a line parallel to x axis and in case of b it is a line parallel to y axis.

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