I can't take this Heat!

A system consists of two chambers, one is filled with a gas of molecules \((P_o,V_o,T_o)\) while, the other chamber is vacuum. The Piston is held by a spring.

Find the heat capacity \(\displaystyle C\)(in J/K) of the system, such that when the gas is released, the piston touches the right wall and the spring is relaxed.

Details and Assumptions:
\(\bullet\) The gas is Monoatomic in nature.
\(\bullet\) \(\displaystyle P_o = 1.5 atm\)
\(\bullet\) \(\displaystyle V_o = 3.5 L\)
\(\bullet\) \(\displaystyle T_o = 227^oC\)
\(\bullet\) \(\displaystyle k = 150 N/m\)


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