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 \( L \) and \( 2L \) are the lengths of the gas column before and after expansion respectively, then \( \frac{T_1}{T_2} \) is

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

Hint:

In adiabatic process, use \( TV^{\gamma-1} = \text{constant} \). For monoatomic gas, \( \gamma = \frac{5}{3} \).

Answer 1

The Correct Option is B