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Dalton's Law of Partial Pressures

1m3 of ideal ...

Question

$1 m^{3}$ of ideal gas (air) at 12 kPa and $100^{\circ} C$ expands isentropically to 3kPa $C_{p} of gas = 1.005 k J / k g K, C_{v} = 0.718 k J / k g K,$ What is the final temperature of the gas $i n^{\circ} F$ ?

-7.6

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-22

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251

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Solution

The correct option is A -7.6
$\frac{T_{2}}{T_{1}} = {(\frac{P_{2}}{P_{1}})}^{γ - 1 / γ} = {(\frac{3}{12})}^{1.4 - 1 / 1.4}$

$T_{2} = T_{1} {(\frac{3}{(} 12))}^{0} .4 / 1, 4 = 373 \times {(\frac{1}{4})}^{0.4 / 1.4}$

$T_{2} = 251.0 K = - 11^{\circ} C$

$^{\circ} F = {\frac{9}{5}}^{\circ} C + 32 = \frac{9}{5} \times (- 22) + 32 = - {7.6}^{\circ} F$

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