A closed adiabatic piston-cylinder apparatus is set up as shown below. The pisto

Question

A closed adiabatic piston-cylinder apparatus is set up as shown below. The piston separates the volume within the cylinder into two partitions. Side A is initially at volume 0.1 m3. Side B is initially 0.2 m3. The cross-sectional area is 0.1 m2. The bottom compartment is initially at saturated steam at 2 bar. The top compartment is air initially at 1 bar. The piston is initially held in place by a mass atop the assembly as shown. At time = zero, the mass is removed, allowing the system to proceed toward equilibrium. Find the mass of the block. Once the block is removed, find the final temperature, the final pressure and the distance the piston has traveled. If we replace the block after the system has reached equilibrium, how much work is put back into the system? If we leave the block on and increase the bottom compartment temperature by 100 degree C, what will be the work done on the piston?

Explanation / Answer

Force by block(mg)= force on the piston due to pressures P1 and P2

mx9.8= (P2-P1)xA

m= (2bar-1bar)x(0.1 m^2)/(9.8 m/s^2)

=0.1x9.8x10^5 kg

= 9.8x10^4 kg

b) Once the block is removed the final pressure in part A is 1 bar

Using PV^1/3 constant,

2x(0.1)^1.3 = 1.V^1.3

V= 0.17 m^3

Ax=V

0.1xX=0.17

X=1.7 m(final one)

Initial X is 0.1/0.1= 1 m

So piston has moved 70 cms

c) Work done(F.X)= 98x10^3x0.7x9.8

= 672.28 kJ

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