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COMEDK · Physics · 13. Thermodynamics

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

  1. A \(\left(\dfrac{1}{2}\right)^{2 / 3}\)
  2. B \(2^{3 / 2}\)
  3. C \(2^{2 / 3}\)
  4. D \(\left(\dfrac{1}{2}\right)^{3 / 2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2^{2 / 3}\)

Step-by-step Solution

Detailed explanation

For an adiabatic process of an ideal gas, the relationship between temperature and volume is given by \(T V^{\gamma - 1} = \text{constant}\). For a monoatomic gas, the adiabatic index \(\gamma = \dfrac{5}{3}\). Thus, \(\gamma - 1 = \dfrac{5}{3} - 1 = \dfrac{2}{3}\). The volume…