Thermodynamics

JEE Main level, single correct, medium

123 of 190

Question 123 of 190

A monoatomic ideal gas, initially at temperature T1{T}_{1} is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2{T}_{2} by releasing the piston suddenly. If l1{l}_{1} and l2{l}_{2} are the lengths of the gas column, before and after the expansion respectively, then the value of T1T2\dfrac{{T}_{1}}{{T}_{2}} will be:

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Answer: (B) (l2l1)23{\left(\dfrac{{l}_{2}}{{l}_{1}}\right)}^{\dfrac{2}{3}}

PVr=P{V}^{r}= constant
TVr−1=T{V}^{r-1}= constant
T(ℓ)53−1=T{(\ell )}^{\dfrac{5}{3}-1}= constant
T1T2=(ℓ2ℓ1)2/3\dfrac{{T}_{1}}{{T}_{2}}={\left(\dfrac{{\ell }_{2}}{{\ell }_{1}}\right)}^{2/3}

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