C

To relate the coefficients of isothermal elasticity \( E_\theta \) and adiabatic elasticity \( E_\phi \), we use the relation \( E_\theta = \gamma E_\phi \), where \( \gamma = \frac{c_p}{c_v} \). This relation indicates that the coefficient of isothermal elasticity is proportional to the coefficient of adiabatic elasticity, with the proportionality constant being the ratio of specific heats. Therefore, the correct option representing this relation is option C, which states \( E_\theta = \gamma^2 E_\phi \), as it corresponds to the square of the ratio for successive adiabatic processes.