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 300K300 K. The compression in the spring is 10 cm10 \text{ cm}. The temperature of the left and the right chambers are now raised slowly to 400K400 K and 500K500 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 (α60m\frac{\alpha}{60}m). Find α\alpha.

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

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