A monoatomic ideal gas, initially at temperature , is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature by releasing the piston suddenly. If and are the length of the gas column before

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 length of the gas column before and after expansion respectively, then $\frac{T_{1}}{T_{2}}$ is given by [2000]

Smart Achievers · Accepted Answer

(4)

$From T V^{γ - 1} = constant$

For monoatomic gas $γ = \frac{5}{3}$ , hence $T V^{2 / 3} = constant$

$∴$ $T_{1} L_{1}^{2 / 3} = T_{2} L_{2}^{2 / 3}$ $(∵ V \propto L)$

Hence, $\frac{T_{1}}{T_{2}} = {(\frac{L_{2}}{L_{1}})}^{2 / 3}$

Solution

1 ${(\frac{L_{1}}{L_{2}})}^{2 / 3}$

2 $\frac{L_{1}}{L_{2}}$

3 $\frac{L_{2}}{L_{1}}$

4 ${(\frac{L_{2}}{L_{1}})}^{2 / 3}$

Ans.
(4)

$From T V^{γ - 1} = constant$

For monoatomic gas $γ = \frac{5}{3}$ , hence $T V^{2 / 3} = constant$

$∴$ $T_{1} L_{1}^{2 / 3} = T_{2} L_{2}^{2 / 3}$ $(∵ V \propto L)$

Hence, $\frac{T_{1}}{T_{2}} = {(\frac{L_{2}}{L_{1}})}^{2 / 3}$

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Solution

1 (L1L2)2/3

2 L1L2

3 L2L1

4 (L2L1)2/3