why is the idea of an ideal gas untrue or not possible
Ideal gas
c ^ V = 1 n R T ( ∂ S ∂ T ) V = 1 n R ( ∂ U ∂ T ) V ( \ displaystyle ( \ hat ( c ) ) _ ( V ) = ( \ frac ( 1 ) ( nR ) ) T \ left ( ( \ frac ( \ partial S ) ( \ partial T ) ) \ right ) _ ( V ) = ( \ frac ( 1 ) ( nR ) ) \ left ( ( \ frac ( \ partial U ) ( \ partial T ) ) \ right ) _ ( V ) )
c ^ V = 1 n R T ( ∂ S ∂ T ) V = 1 n R ( ∂ U ∂ T ) V ( \ displaystyle ( \ hat ( c ) ) _ ( V ) = ( \ frac ( 1 ) ( nR ) ) T \ left ( ( \ frac ( \ partial S ) ( \ partial T ) ) \ right ) _ ( V ) = ( \ frac ( 1 ) ( nR ) ) \ left ( ( \ frac ( \ partial U ) ( \ partial T ) ) \ right ) _ ( V ) )