An insulated box containing ideal gas having $C_{p} = 1 k J / k g K$ and $R = 0.30 k J / k g K$ falls from a height of 2 km above the surface of the earth. What is the temperature rise of the gas after the box hits the ground ?

0 K

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14 K

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28 K

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36 K

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Solution

The correct option is C 28 K
$C_{P} - R = C_{v}$

$1 - 0.30 = C_{v} = 0.70 k J / K g K$

$From energy conservation$

$Δ U = Change in potential energy$

$m c_{v} Δ T = m g h$

$Δ T = \frac{g h}{C_{v}} = \frac{9.81 \times 2000}{0.70 \times 10^{5}}$

$Δ = 28 K$

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