A cylinder of $$cross-section$$ area A has two pistons of negligible mass separated by distances l loaded with spring negligible mass. An ideal gas at temperature $$T1$$ is in the cylinder where the springs are relaxed. When the gas is heated by some means its temperature becomes $$T2$$ and the springs get compressed by $$l2$$ each. If $$P0$$ is atmospheric pressure and spring constant $$k=2P0Al$$ then the ratio of $$T2$$ and $$T1$$ is $$_______$$

Question

A cylinder of $$cross-section$$ area A has two pistons of negligible mass separated by distances l loaded with spring negligible mass. An ideal gas at temperature $$T1$$ is in the cylinder where the springs are relaxed. When the gas is heated by some means its temperature becomes $$T2$$ and the springs get compressed by $$l2$$ each. If $$P0$$ is atmospheric pressure and spring constant $$k=2P0Al$$ then the ratio of $$T2$$ and $$T1$$ is $$_______$$

Infinity Learn · Accepted Answer

$$P1V1T1=P2V2T2$$ where $$V1=lA$$ and $$V2=2lA$$ and $$P1=P0$$ and $$P2=kxA+P0=2P0All2A+P0=2P0$$∵$$x=l2$$⇒$$T2T1=P2V2P1V1=2P02lAP0lA=4$$

Introduction-thermodynamics

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P1V1T1=P2V2T2 where V1=lA and V2=2lA and P1=P0 and P2=kxA+P0=2P0All2A+P0=2P0∵x=l2⇒T2T1=P2V2P1V1=2P02lAP0lA=4

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