A given ideal gas with gamma = frac{{{Cₚ}}}{{{Cᵥ}}} = 1.5 at a temperatur

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11.Thermodynamics

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A given ideal gas with $\gamma = \frac{{{C_p}}}{{{C_v}}} = 1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be ..... $T$

A

$2\sqrt 2$

B

$4$

C

$2$

D

$8$

(AIEEE-2012)

Solution

$T V^{\gamma-1}=\text { constant }$

$T_{1} V_{1}^{\gamma-1}=\mathrm{T}_{2} V_{2}^{\gamma-1}$

$\Rightarrow T(V)^{1 / 2}=\mathrm{T}_{2}\left(\frac{V}{4}\right)^{1 / 2}$

$\left[\because \gamma=1.5, T_{1}=T, V_{1}=V \text { and } V_{2}=\frac{V}{4}\right]$

$\therefore \quad T_{2}=\left(\frac{4 V}{V}\right)^{1 / 2} T=2 T$

Standard 11

Physics

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