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MHT CET · Physics · Thermodynamics

A monoatomic ideal gas, initially at temperature \(T_1\) is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature \(T_2\). If \(L_1\) and \(L_2\) are the lengths of the gas columns before and after expansion respectively, then \(\left(T_2 / T_1\right)\) is given by

  1. A \(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\)
  2. B \(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\)
  3. C \(\left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{2 / 3}\)
  4. D \(\left(\frac{\mathrm{L}_2}{\mathrm{~L}_1}\right)^{2 / 3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\right)^{2 / 3}\)

Step-by-step Solution

Detailed explanation

\(T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}\) \(\frac{T_2}{T_1} = \left(\frac{V_1}{V_2}\right)^{\gamma-1} = \left(\frac{L_1}{L_2}\right)^{\gamma-1}\)