First slide

Different type of processes

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 teh lengths of the gas column before and after expansion respectively, then $T_{1}$ / $T_{2}$ is given by

Easy

A

$\left (\frac{L_1}{L_2} \right )^\frac{2}{3}$
B

L₁/L₂
C

L₂/L₁
D

$\left (\frac{L_2}{L_1} \right )^\frac{2}{3}$

Solution

γ = 5/3
TV^γ-1= K⇒Tα 1/v^γ-1
$\frac{{{T_1}}}{{{T_2}}} = {\left( {\frac{{{V_2}}}{{{V_1}}}} \right)^{\gamma - 1}}$
But V = AL; A is constant
VαL
$\frac{{{T_1}}}{{{T_2}}} = {\left( {\frac{{{L_2}}}{{{L_1}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 2$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}}}$

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