A monatomic ideal gas, initially at temperature $$T1$$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $$T2$$ by releasing the piston suddenly. If $$L1$$ and $$L2$$ are the length of the gas column before and after expansion respectively, then $$T1T2is$$ given by

Question

A monatomic ideal gas, initially at temperature $$T1$$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $$T2$$ by releasing the piston suddenly. If $$L1$$ and $$L2$$ are the length of the gas column before and after expansion respectively, then $$T1T2is$$ given by

Infinity Learn · Accepted Answer

Here TVγ−$$1=$$ constant As γ$$=5/3$$,hence $$TV2/3=$$ constant Now, $$T1L12/3=T2L22/3$$ $$($$∵V∝$$L)or$$     $$T1T2=L2L12/3$$

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