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Heat Capacity at Constant Pressure

The differenc...

Question

The difference between $C_{p}$ and $C_{v}$ can be derived using $H = U + P V$ . Calculate the difference between $C_{p}$ and $C_{v}$ for 10 moles of an ideal gas.

A

41.84 J/K

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B

71.48 J/K

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C

23.65 J/K

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D

83.14 J/K

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Solution

The correct option is D 83.14 J/K
From first law, $Δ U = q + w$
For a constant volume system, w = 0 and $Δ U = n C_{v} d T$ = heat at constant volume
where n is the number of moles of the gas
Similarly, $Δ H = n C_{p} d T$ = Heat at constant pressure
We know, $C_{p} -$ $C_{v}$ = R for 1 mole of a gas
Similarly, $C_{p} -$ $C_{v}$ = nR for n mole of a gas
$C_{p} -$ $C_{v}$ = $10 \times 8.314$ $J m o l^{- 1} K^{- 1}$
= 83.14 J/K

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Heat Capacity at Constant Pressure

Standard XIII Chemistry

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