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 the expansion respectively, then the value of (T1/T2) will be:

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 the expansion respectively, then the value of (T1/T2) will be: (A) ((l1/l2))(2/3) (B) ((l2/l1))(2/3) (C) (l2/l1) (D) (l1/l2)

Tardigrade Admin · Accepted Answer

P Vr= const T Vr-1= const. T(l)(5/3)-1= const (T1/T2)=((l2/l1))2 / 3

$(\frac{l _{1}}{l _{2}})^{\frac{2}{3}}$

$(\frac{l _{2}}{l _{1}})^{\frac{2}{3}}$

$\frac{l _{2}}{l _{1}}$

$\frac{l _{1}}{l _{2}}$

$P V^{r} =$ const
$T V^{r - 1} =$ const.
$T (l)^{\frac{5}{3} - 1} =$ const
$\frac{T _{1}}{T _{2}} = (\frac{l _{2}}{l _{1}})^{2/3}$

(l2​l1​​)32​

(l1​l2​​)32​

l1​l2​​

l2​l1​​

PVr= const TVr−1= const. T(l)35​−1= const T2​T1​​=(l1​l2​​)2/3

$(\frac{l _{1}}{l _{2}})^{\frac{2}{3}}$

$(\frac{l _{2}}{l _{1}})^{\frac{2}{3}}$

$\frac{l _{2}}{l _{1}}$

$\frac{l _{1}}{l _{2}}$

$P V^{r} =$ const
$T V^{r - 1} =$ const.
$T (l)^{\frac{5}{3} - 1} =$ const
$\frac{T _{1}}{T _{2}} = (\frac{l _{2}}{l _{1}})^{2/3}$