A diatomic ideal gas is compressed adiabatically to \frac{1}{32} of its initial volume. In the initial temperature of gas is Ti (in Kelvin) and the final temperature is \alphaTi, the value of α is

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Physics

Scalar Triple Product

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A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. In the initial temperature of gas is T_i (in Kelvin) and the final temperature is $α$ T_i, the value of α is

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$T_{0} V_{0}^{7 / 5} = T {(\frac{V_{0}}{32})}^{7 / 5} = T {(\frac{V_{0}}{32})}^{2 / 5}$

$I = T_{0} \times (32^{2 / 5}) = 4 T_{0}$

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