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Heat Capacity

When 229J o...

Question

When $229 J$ of energy is supplied as heat at constant pressure to $3$ mol $A r (g)$ , the temperature of the sample is increased by $2.55 K$ . Calculate the molar heat capacity at constant volume:

A

30 K J K^{- 1} {m o l}^{- 1}

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B

30 J K^{- 1} {m o l}^{- 1}

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C

21.7 J K^{- 1} {m o l}^{- 1}

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D

21.7 K J K^{- 1} {m o l}^{- 1}

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Solution

The correct option is A $21.7 J K^{- 1} {m o l}^{- 1}$
$C p - C v = n R$

$C p = q / Δ T$

$C p = 229 J / 2.55 K$ $= 89.80 J k^{- 1}$

$C v = C p - n R = 89.80 - (3 \times 8.314) = 64.86 J k^{- 1}$

$C v$ per mol $= 64.86 / 3 = 21.6 J k^{- 1} m o l^{- 1}$

$21.6 J k^{- 1} m o l l^{- 1}$

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