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Enthalpy

Which one amo...

Question

Which one among the following is the correct option for right relationship between $C_{P} and C_{V}$ for one mole of ideal gas?

A

C_{V} = R C_{P}

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B

C_{P} + C_{V} = R

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C

C_{P} - C_{V} = R

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D

C_{P} = R C_{V}

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Solution

The correct option is C $C_{P} - C_{V} = R$
At constant volume, $q_{V} = C_{V} Δ T = Δ U$
At constant pressure, $q_{P} = C P Δ T = Δ H$
For a mole of an ideal gas,
$Δ H = Δ U + Δ (P V)$
$= Δ U + Δ (R T)$
$= Δ U + R Δ T$

On putting the values of $Δ H a n d Δ U$ , we have $C_{P} Δ T = C_{V} Δ T + R Δ T$
$C_{P} = C_{V} + R$
$C_{P} - C_{V} = R$

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