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Relating Translational KE and T

Two moles of ...

Question

Two moles of an ideal gas $(C_{v, m} = 12.5 J K^{- 1} m o l^{- 1})$ are at $300 K$ and $5 d m^{3}$ . If the gas is heated to $600 K$ and the volume changed to $10 d m^{3}$ , calculate the entropy change.
(take ln2=0.7, $R = 8.3 J m o l^{- 1} K^{- 1}$ )

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Solution

The entropy changes as function of $T$ and $V$ is,

$△ S = n C_{v, m} l n \frac{T_{2}}{T_{1}} + n R l n \frac{V_{2}}{V_{1}}$

$△ S = (2 m o l) \times (12.5 J K^{- 1} m o l - 1) l n \frac{600}{300} + (2 m o l) \times (8.3 J K^{- 1} m o l^{- 1}) l n \frac{10}{5}$
$= 17.5 J K^{- 1} + 11.62 J K^{- 1}$
$= 29.12 J K^{- 1}$

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C_{V, m} = 12.5 J K^{- 1} m o l^{- 1}

d m^{3}

d m^{3}

10 moles of an ideal gas expands adiabatically reversibly from 5 $d m^{3}$ to 10 $d m^{3}$ at 300 K. Find the entropy change.

(C_{p . m} = \frac{5}{2} R)

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127^{\circ} C

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R = 8.3 {J K}^{- 1} {mol}^{- 1}

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O_{2}

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400 K

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