The left and right compartments of a thermally isolated container of length L are separated by a thermally conducting, movable piston of area A. The left and right compartments are filled with 32 and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant k and natural length 2L5. In thermodynamic equilibrium, the piston is at a distance L2 from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is P= kLA , then the value of is [figure]
Answer
0.2
Solution
Conducting piston: both gases at the same T; equal volumes AL2, so P n: PL= 32P.
Spring length L2 vs natural 2L5: stretched by L10, pulls the piston to the left with force kL10.
Piston equilibrium: PLA=PA+ kL10 12PA= kL10
P= kL5A =0.2
Answer: 0.2