Question 40: Thermodynamics & KTG

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 $\mathrm{T}_2$ by releasing the piston suddenly. If $L$ and $2 L$ are the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is

Accepted Answer

For a (reversible) adiabatic expansion of a monoatomic ideal gas (ÃÂ³ = 5/3) one has
$$T\,V^{\,ÃÂ³-1}=	ext{constant}\,. $$
Since the volume doubles (VÃ¢ÂÂ/VÃ¢ÂÂ = 2),
$$\frac{T_1}{T_2}=\Bigl(\frac{V_2}{V_1}\Bigr)^{ÃÂ³-1} =2^{\,	frac{5}{3}-1} =2^{2/3}\,. $$
Answer: Option B.

Answer

$2^{3 / 2}$

Answer

$2^{2 / 3}$

Answer

$\left(\frac{1}{2}\right)^{2 / 3}$

Answer

$\left(\frac{1}{2}\right)^{3 / 2}$

Thermodynamics & KTG

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