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 L2 are the lengths of the gas column before and after expansion respectively, then T1 / T2 is given by

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 L2 are the lengths of the gas column before and after expansion respectively, then T1 / T2 is given by (A) (L1 /L2)2/3 (B) (L1 /L2) (C) L2/L1 (D) (L2 /L1)2/3

Tardigrade Admin · Accepted Answer

During adiabatic expansion, we known TV&gamma; -1= constant or T1 V1&gamma;-1=T2V2&gamma;-1 For a monoatomic gas &gamma;=(5/3) ∴ (T1/T2)=((V2/V1))&gamma;-1 =((AL2/AL1))(5/3)-1 (A = Area of cross-section of piston) =((L2/L1))2/3

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

$(L_{1} / L_{2})$

$L_{2} / L_{1}$

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

(L1​/L2​)2/3

(L1​/L2​)

L2​/L1​

(L2​/L1​)2/3

During adiabatic expansion, we known TVγ−1= constant or T1​V1γ−1​=T2​V2γ−1​ For a monoatomic gas γ=35​ ∴T2​T1​​=(V1​V2​​)γ−1=(AL1​AL2​​)(5/3)−1 (A = Area of cross-section of piston) =(L1​L2​​)2/3

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

$(L_{1} / L_{2})$

$L_{2} / L_{1}$

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