# Editing Ideal gas: Heat capacity

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where <math>U</math> is the [[internal energy]]. Given that an [[ideal gas]] has no interatomic potential energy, the only term that is important is the [[Ideal gas: Energy | kinetic energy of an ideal gas]], which is equal to <math>(3/2)RT</math>. Thus | where <math>U</math> is the [[internal energy]]. Given that an [[ideal gas]] has no interatomic potential energy, the only term that is important is the [[Ideal gas: Energy | kinetic energy of an ideal gas]], which is equal to <math>(3/2)RT</math>. Thus | ||

β | :<math>C_V = \frac{\partial ~ }{\partial T} \left( \frac{3}{2}RT \right) = \frac{3}{2} R </math> | + | :<math>C_V = \frac{\partial ~ }{\partial T} \left( \frac{3}{2}RT \right) = \frac{3}{2} R </math>. |

At constant [[pressure]] one has | At constant [[pressure]] one has | ||

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thus | thus | ||

β | + | {{resultbox|<math>C_p = C_v + R = \frac{5}{2} R</math>}} | |

where <math>R</math> is the [[molar gas constant]]. | where <math>R</math> is the [[molar gas constant]]. |