A monoatomic ideal gas,initially at temperatu | vedclass

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(B) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Since the gas is m

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

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(B) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Since the gas is monoatomic,the adiabatic index $\gamma = \frac{5}{3}$.Therefore,$\gamma - 1 = \frac{5}{3} - 1 = \frac{2}{3}$.The volume of the gas column in a cylinder of cross-sectional area $A$ is $V = A 	imes L$.Thus,$T_1 (A L_1)^{\gamma-1} = T_2 (A L_2)^{\gamma-1}$.Rearranging for the ratio $\frac{T_1}{T_2}$,we get:$\frac{T_1}{T_2} = \left(\frac{L_2}{L_1}ight)^{\gamma-1} = \left(\frac{L_2}{L_1}ight)^{2/3}$.

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