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 the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be:

• A. $\left(\frac{l_{1}}{l_{2}}\right)^{\frac{2}{3}}$
• B. $\left(\frac{l_{2}}{l_{1}}\right)^{\frac{2}{3}}$
• C. $\frac{l_{2}}{l_{1}}$
• D. $\frac{l_{1}}{l_{2}}$

Answer 1

Answer: (B)

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