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The magnetic susceptibility $\chi(T)$ of spin-1/2 chains is widely used toquantify exchange interactions, even though $\chi(T)$ is similar for differentcombinations of ferromagnetic $J_1$ between first neighbors andantiferromagnetic $J_2$ between second neighbors. We point out that the spinspecific heat $C(T)$ directly determines the ratio $\alpha = J_2/|J_1|$ ofcompeting interactions. The $J_1-J_2$ model is used to fit the isothermalmagnetization $M(T,H)$ and $C(T,H)$ of spin-1/2 Cu(II) chains in LiCuSbO$_4$.By fixing $\alpha$, $C(T)$ resolves the offsetting $J_1$, $\alpha$ combinationsobtained from $M(T,H)$ in cuprates with frustrated spin chains.

Spin-specific heat determination of the ratio of competing first- and second-neighbor exchange interactions in frustrated spin-$\frac{1}{2}$ chains