Find the Compression!

Consider the diagram shown above where the two chambers separated by piston-spring arrangement contain equal amounts of same ideal gas. Initially when the temperatures of the gas in both the chambers are kept at \(300 K\). The compression in the spring is \(10 \text{ cm}\). The temperature of the left and the right chambers are now raised slowly to \(400 K\) and \(500 K\) respectively. The pistons are free to slide (i.e. no friction between piston and chamber). Final compression in the spring is found to be (\(\frac{\alpha}{60}m\)). Find \(\alpha\).

Use \(\sqrt{481} = 22 \).

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