First slide

Different type of processes

Question

A monoatomic 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 L₂are lengths of the gas column before and after expansion respectively, then T₁/T₂ is given by

Moderate

A

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

${(\frac{L_{1}}{L_{2}})}^{5 / 3}$
C

${(\frac{L_{2}}{L_{1}})}^{5 / 3}$
D

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

Solution

In adiabatic process, $T V^{γ - 1} = constant$
$∴ \frac{T_{1}}{T_{2}} = {(\frac{V_{2}}{V_{1}})}^{γ - 1} = {(\frac{A L_{2}}{A L_{1}})}^{5 / 3 - 1} = {(\frac{L_{2}}{L_{1}})}^{2 / 3}$

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