$C_{p} - C_{v}$ for an ideal gas is ______.

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Solution

For an ideal gas,
$△ H = Q_{P} = n C_{P} △ T$ $△ U = Q_{V} = n C_{V} △ T$
$△ H = △ U + R △ T$
$n C_{p} △ T = n C_{V} △ T + R △ T$
$n △ T (C_{P} - C_{V}) = R △ T ⟶ C_{P} - C_{V} = R$

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