1. Tardigrade
  2. Question
  3. Physics
  4. A monatomic 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 length of the gas column before and after expansion respectively, then (T1/T2) is given by

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Q. A monatomic 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 length of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is given by

Thermodynamics

Solution:

Here $T V^{\gamma-1}=$ constant
As $\gamma=\frac{5}{3}$, hence $T V^{2 / 3}=$ constant
Now $T_1 L_1^{2 / 3}=T_2 L_2^{2 / 3}(\because V \propto L)$;
Hence, $\frac{T_1}{T_2}=\left(\frac{L_2}{L_1}\right)^{2 / 3}$