First law for isobaric processes

𝑑 𝑊 = - 𝑝 𝑑 𝑉 𝑑 𝑄 = 𝑛 𝐶 𝑝 𝑑 𝑇

where

$𝐶 𝑝 : J \cdot m o l - 1 \cdot K - 1$ is the molar specific heat for gas of constant pressure

For ideal gas

By the Ideal gas law, if $𝑝$ is constant,

𝑑 𝑉 = 𝑛 𝑅 𝑝 𝑑 𝑇

and therefore

𝑑 𝑊 = - 𝑛 𝑅 𝑑 𝑇 𝑑 𝑈 = 𝑑 𝑄 + 𝑑 𝑊 = 𝑛 𝐶 𝑝 𝑑 𝑇 - 𝑅 𝑑 𝑇

which, using the equation from First law for isovolumetric processes, shows

𝑛 𝐶 𝑉 𝑑 𝑇 = 𝑛 𝐶 𝑝 𝑑 𝑇 - 𝑅 𝑑 𝑇 𝐶 𝑉 = 𝐶 𝑝 - 𝑅

As a consequence of the above, for a monatomic ideal gas

𝐶 𝑝 = 52 𝑅

#state/tidy | #SemBr