1 mole of an ideal gas is enclosed in a metal cylindrical container (radius = 10
ID: 1275567 • Letter: 1
Question
1 mole of an ideal gas is enclosed in a metal cylindrical container (radius = 10 cm) with a frictionless, light, movable piston with a mass of lkg on top of it and is in contact with a thermal bath at T = 400 C. At what height is the piston (from the base of the container), at equilibrium? Work is done, slowly, while keeping the cylinder in contact with the thermal bath to compress the volume by 1/3rd of its initial volume. How much work was done to achieve this? What happened to this work (or where did it go)?Explanation / Answer
at equilirum pressure exerted by 1kg of block will be the equilibrium pressure.
force=1kg*9.8 m/sec^2=9.8N
area=pi*r*r;
pressure=force/area
ideal gas equation=pv=nrt
(9.8/pi*r*r)(vol of cylinder)=1*.0821*673; vol of cylinder=pi*r*r*h;
height of cyclinder=5.63m
work done =p*(v2-v1) =(9.8/pi*r*r ) *(2/3)*vol of cylinder
36.782J (this work done will lead to volume compression and increase in internal energy in form of temperature )
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