A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion…

Question

A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is given by

Aicharya · Accepted Answer

During adiabatic expansion, we know TV γ - 1 = constant or T 1 V 1 γ - 1 = T 2 V 2 γ - 1 For a monoatomic gas, γ = 5 3 ∴ T 1 T 2 = V 2 V 2 γ - 1 = AL 2 AL 1 5 / 3 -1 (where A is the cross section area of the piston) = L 2 L 1 2 / 3

A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless…

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